Classes of numbers

## Basic

Positive integers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, …

Whole numbers (or nonnegative integers): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, …

Even numbers: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68,70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, …

Odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, …

## By omega(n) and biomega(n)

Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, …

Composite numbers: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, …

Prime powers: 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 243, 251, 256, 257, 263, 269, 271, 277, 281, 283, 289, 293, 307, 311, 313, 317, 331, 337, 343, 347, 349, 353, 359, 361, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 512, 521, 523, 529, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 625, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 729, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 841, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 961, 967, 971, 977, 983, 991, 997, …

True prime powers: 4, 8, 9, 16, 25, 27, 32, 49, 64, 81, 121, 125, 128, 169, 243, 256, 289, 343, 361, 512, 529, 625, 729, 841, 961, 1024, 1331, 1369, 1681, 1849, 2048, 2187, 2197, 2209, 2401, 2809, 3125, 3481, 3721, 4096, 4489, 4913, 5041, 5329, 6241, 6561, 6859, 6889, 7921, 8192, 9409, …

Semiprimes (2-almost primes): 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39, 46, 49, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 121, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 169, 177, 178, 183, 185, 187, 194, 201, 202, 203, 205, 206, 209, 213, 214, 215, 217, 218, 219, 221, 226, 235, 237, 247, 249, 253, 254, 259, 262, 265, 267, 274, 278, 287, 289, 291, 295, 298, 299, 301, 302, 303, 305, 309, 314, 319, 321, 323, 326, 327, 329, 334, 335, 339, 341, 346, 355, 358, 361, 362, 365, 371, 377, 381, 382, 386, 391, 393, 394, 395, 398, 403, 407, 411, 413, 415, 417, 422, 427, 437, 445, 446, 447, 451, 453, 454, 458, 466, 469, 471, 473, 478, 481, 482, 485, 489, 493, 497, 501, 502, 505, 511, 514, 515, 517, 519, 526, 527, 529, 533, 535, 537, 538, 542, 543, 545, 551, 553, 554, 559, 562, 565, 566, 573, 579, 581, 583, 586, 589, 591, 597, 611, 614, 622, 623, 626, 629, 633, 634, 635, 649, 655, 662, 667, 669, 671, 674, 679, 681, 685, 687, 689, 694, 695, 697, 698, 699, 703, 706, 707, 713, 717, 718, 721, 723, 731, 734, 737, 745, 746, 749, 753, 755, 758, 763, 766, 767, 771, 778, 779, 781, 785, 789, 791, 793, 794, 799, 802, 803, 807, 813, 815, 817, 818, 831, 835, 838, 841, 842, 843, 849, 851, 862, 865, 866, 869, 871, 878, 879, 886, 889, 893, 895, 898, 899, 901, 905, 913, 914, 917, 921, 922, 923, 926, 933, 934, 939, 943, 949, 951, 955, 958, 959, 961, 965, 973, 974, 979, 982, 985, 989, 993, 995, 998, …

3-almost primes: 8, 12, 18, 20, 27, 28, 30, 42, 44, 45, 50, 52, 63, 66, 68, 70, 75, 76, 78, 92, 98, 99, 102, 105, 110, 114, 116, 117, 124, 125, 130, 138, 147, 148, 153, 154, 164, 165, 170, 171, 172, 174, 175, 182, 186, 188, 190, 195, 207, 212, 222, 230, 231, 236, 238, 242, 244, 245, 246, 255, 258, 261, 266, 268, 273, 275, 279, 282, 284, 285, 286, 290, 292, 310, 316, 318, 322, 325, 332, 333, 338, 343, 345, 354, 356, 357, 363, 366, 369, 370, 374, 385, 387, 388, 399, 402, 404, 406, 410, 412, 418, 423, 425, 426, 428, 429, 430, 434, 435, 436, 438, 442, 452, 455, 465, 470, 474, 475, 477, 483, 494, 498, 506, 507, 508, 518, 524, 530, 531, 534, 539, 548, 549, 555, 556, 561, 574, 575, 578, 582, 590, 595, 596, 598, 602, 603, 604, 605, 606, 609, 610, 615, 618, 627, 628, 637, 638, 639, 642, 645, 646, 651, 652, 654, 657, 658, 663, 665, 668, 670, 678, 682, 692, 705, 710, 711, 715, 716, 722, 724, 725, 730, 741, 742, 747, 754, 759, 762, 764, 772, 775, 777, 782, 786, 788, 790, 795, 796, 801, 805, 806, 814, 822, 826, 830, 833, 834, 844, 845, 847, 854, 861, 867, 873, 874, 885, 890, 892, 894, 897, 902, 903, 906, 908, 909, 915, 916, 925, 927, 931, 932, 935, 938, 942, 946, 956, 957, 962, 963, 964, 969, 970, 978, 981, 986, 994, …

4-almost primes: 16, 24, 36, 40, 54, 56, 60, 81, 84, 88, 90, 100, 104, 126, 132, 135, 136, 140, 150, 152, 156, 184, 189, 196, 198, 204, 210, 220, 225, 228, 232, 234, 248, 250, 260, 276, 294, 296, 297, 306, 308, 315, 328, 330, 340, 342, 344, 348, 350, 351, 364, 372, 375, 376, 380, 390, 414, 424, 441, 444, 459, 460, 462, 472, 476, 484, 488, 490, 492, 495, 510, 513, 516, 522, 525, 532, 536, 546, 550, 558, 564, 568, 570, 572, 580, 584, 585, 620, 621, 625, 632, 636, 644, 650, 664, 666, 676, 686, 690, 693, 708, 712, 714, 726, 732, 735, 738, 740, 748, 765, 770, 774, 776, 783, 798, 804, 808, 812, 819, 820, 824, 825, 836, 837, 846, 850, 852, 855, 856, 858, 860, 868, 870, 872, 875, 876, 884, 904, 910, 930, 940, 948, 950, 954, 966, 975, 988, 996, 999, …

5-almost primes: 32, 48, 72, 80, 108, 112, 120, 162, 168, 176, 180, 200, 208, 243, 252, 264, 270, 272, 280, 300, 304, 312, 368, 378, 392, 396, 405, 408, 420, 440, 450, 456, 464, 468, 496, 500, 520, 552, 567, 588, 592, 594, 612, 616, 630, 656, 660, 675, 680, 684, 688, 696, 700, 702, 728, 744, 750, 752, 760, 780, 828, 848, 882, 888, 891, 918, 920, 924, 944, 945, 952, 968, 976, 980, 984, 990, …

6-almost primes: 64, 96, 144, 160, 216, 224, 240, 324, 336, 352, 360, 400, 416, 486, 504, 528, 540, 544, 560, 600, 608, 624, 729, 736, 756, 784, 792, 810, 816, 840, 880, 900, 912, 928, 936, 992, 1000, 1040, 1104, 1134, 1176, 1184, 1188, 1215, 1224, 1232, 1260, 1312, 1320, 1350, 1360, 1368, 1376, 1392, 1400, 1404, 1456, 1488, 1500, 1504, 1520, 1560, 1656, 1696, 1701, 1764, 1776, 1782, 1836, 1840, 1848, 1888, 1890, 1904, 1936, 1952, 1960, 1968, 1980, 2025, 2040, 2052, 2064, 2088, 2100, 2106, 2128, 2144, 2184, 2200, 2232, 2250, 2256, 2272, 2280, 2288, 2320, 2336, 2340, 2480, 2484, 2500, 2528, 2544, 2576, 2600, 2646, 2656, 2664, 2673, 2704, 2744, 2754, 2760, 2772, 2832, 2835, 2848, 2856, 2904, 2928, 2940, 2952, 2960, 2970, 2992, 3060, 3078, 3080, 3096, 3104, 3132, 3150, 3159, 3192, 3216, 3232, 3248, 3276, 3280, 3296, 3300, 3344, 3348, 3375, 3384, 3400, 3408, 3420, 3424, 3432, 3440, 3472, 3480, 3488, 3500, 3504, 3510, 3536, 3616, 3640, 3720, 3726, 3750, 3760, 3792, 3800, 3816, 3864, 3900, 3952, 3969, 3984, 3996, 4048, 4056, 4064, 4116, 4131, 4140, 4144, 4158, 4192, 4240, 4248, 4272, 4284, 4312, 4356, 4384, 4392, 4410, 4428, 4440, 4448, 4455, 4488, 4590, 4592, 4600, 4617, 4620, 4624, 4644, 4656, 4698, 4720, 4725, 4760, 4768, 4784, 4788, 4816, 4824, 4832, 4840, 4848, 4872, 4880, 4900, 4914, 4920, 4944, 4950, 5016, 5022, 5024, 5076, 5096, 5100, 5104, 5112, 5130, 5136, 5148, 5160, 5168, 5208, 5216, 5220, 5232, 5250, 5256, 5264, 5265, 5304, 5320, 5344, 5360, 5424, 5456, 5460, 5500, 5536, 5580, 5589, 5625, 5640, 5680, 5688, 5700, 5720, 5724, 5728, 5776, 5792, 5796, 5800, 5840, 5850, 5928, 5936, 5976, 5994, 6032, 6072, 6084, 6096, 6112, 6174, 6176, 6200, 6210, 6216, 6237, 6250, 6256, 6288, 6304, 6320, 6360, 6368, 6372, 6408, 6426, 6440, 6448, 6468, 6500, 6512, 6534, 6576, 6588, 6608, 6615, 6640, 6642, 6660, 6664, 6672, 6732, 6752, 6760, 6776, 6832, 6860, 6885, 6888, 6900, 6930, 6936, 6966, 6984, 6992, 7047, 7080, 7120, 7136, 7140, 7152, 7176, 7182, 7216, 7224, 7236, 7248, 7260, 7264, 7272, 7308, 7320, 7328, 7350, 7371, 7380, 7400, 7416, 7425, 7448, 7456, 7480, 7504, 7524, 7533, 7536, 7568, 7614, 7644, 7648, 7650, 7656, 7668, 7695, 7696, 7700, 7704, 7712, 7722, 7740, 7752, 7760, 7812, 7824, 7830, 7848, 7875, 7884, 7888, 7896, 7952, 7956, 7980, 8008, 8016, 8032, 8040, 8080, 8120, 8136, 8176, 8184, 8190, 8200, 8224, 8240, 8250, 8272, 8304, 8360, 8370, 8416, 8432, 8460, 8464, 8500, 8520, 8528, 8532, 8550, 8560, 8580, 8586, 8592, 8600, 8608, 8664, 8672, 8680, 8688, 8694, 8700, 8720, 8750, 8760, 8775, 8816, 8840, 8848, 8864, 8892, 8904, 8944, 8964, 8991, 8992, 9016, 9040, 9048, 9056, 9100, 9108, 9126, 9144, 9168, 9261, 9264, 9296, 9300, 9315, 9324, 9328, 9375, 9376, 9384, 9400, 9424, 9432, 9456, 9464, 9480, 9500, 9540, 9552, 9558, 9604, 9612, 9639, 9660, 9672, 9702, 9750, 9768, 9776, 9801, 9824, 9864, 9880, 9882, 9912, 9952, 9960, 9963, 9968, 9990, 9996, …

7-almost primes: 128, 192, 288, 320, 432, 448, 480, 648, 672, 704, 720, 800, 832, 972, 1008, 1056, 1080, 1088, 1120, 1200, 1216, 1248, 1458, 1472, 1512, 1568, 1584, 1620, 1632, 1680, 1760, 1800, 1824, 1856, 1872, 1984, 2000, 2080, 2187, 2208, 2268, 2352, 2368, 2376, 2430, 2448, 2464, 2520, 2624, 2640, 2700, 2720, 2736, 2752, 2784, 2800, 2808, 2912, 2976, 3000, 3008, 3040, 3120, 3312, 3392, 3402, 3528, 3552, 3564, 3645, 3672, 3680, 3696, 3776, 3780, 3808, 3872, 3904, 3920, 3936, 3960, 4050, 4080, 4104, 4128, 4176, 4200, 4212, 4256, 4288, 4368, 4400, 4464, 4500, 4512, 4544, 4560, 4576, 4640, 4672, 4680, 4960, 4968, 5000, 5056, 5088, 5103, 5152, 5200, 5292, 5312, 5328, 5346, 5408, 5488, 5508, 5520, 5544, 5664, 5670, 5696, 5712, 5808, 5856, 5880, 5904, 5920, 5940, 5984, 6075, 6120, 6156, 6160, 6192, 6208, 6264, 6300, 6318, 6384, 6432, 6464, 6496, 6552, 6560, 6592, 6600, 6688, 6696, 6750, 6768, 6800, 6816, 6840, 6848, 6864, 6880, 6944, 6960, 6976, 7000, 7008, 7020, 7072, 7232, 7280, 7440, 7452, 7500, 7520, 7584, 7600, 7632, 7728, 7800, 7904, 7938, 7968, 7992, 8019, 8096, 8112, 8128, 8232, 8262, 8280, 8288, 8316, 8384, 8480, 8496, 8505, 8544, 8568, 8624, 8712, 8768, 8784, 8820, 8856, 8880, 8896, 8910, 8976, 9180, 9184, 9200, 9234, 9240, 9248, 9288, 9312, 9396, 9440, 9450, 9477, 9520, 9536, 9568, 9576, 9632, 9648, 9664, 9680, 9696, 9744, 9760, 9800, 9828, 9840, 9888, 9900, …

8-almost primes: 256, 384, 576, 640, 864, 896, 960, 1296, 1344, 1408, 1440, 1600, 1664, 1944, 2016, 2112, 2160, 2176, 2240, 2400, 2432, 2496, 2916, 2944, 3024, 3136, 3168, 3240, 3264, 3360, 3520, 3600, 3648, 3712, 3744, 3968, 4000, 4160, 4374, 4416, 4536, 4704, 4736, 4752, 4860, 4896, 4928, 5040, 5248, 5280, 5400, 5440, 5472, 5504, 5568, 5600, 5616, 5824, 5952, 6000, 6016, 6080, 6240, 6561, 6624, 6784, 6804, 7056, 7104, 7128, 7290, 7344, 7360, 7392, 7552, 7560, 7616, 7744, 7808, 7840, 7872, 7920, 8100, 8160, 8208, 8256, 8352, 8400, 8424, 8512, 8576, 8736, 8800, 8928, 9000, 9024, 9088, 9120, 9152, 9280, 9344, 9360, 9920, 9936, 10000, …

9-almost primes: 512, 768, 1152, 1280, 1728, 1792, 1920, 2592, 2688, 2816, 2880, 3200, 3328, 3888, 4032, 4224, 4320, 4352, 4480, 4800, 4864, 4992, 5832, 5888, 6048, 6272, 6336, 6480, 6528, 6720, 7040, 7200, 7296, 7424, 7488, 7936, 8000, 8320, 8748, 8832, 9072, 9408, 9472, 9504, 9720, 9792, 9856, …

10-almost primes: 1024, 1536, 2304, 2560, 3456, 3584, 3840, 5184, 5376, 5632, 5760, 6400, 6656, 7776, 8064, 8448, 8640, 8704, 8960, 9600, 9728, 9984, …

Squarefree numbers: 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113, 114, 115, 118, 119, 122, 123, 127, 129, 130, 131, 133, 134, 137, 138, 139, 141, 142, 143, 145, 146, 149, 151, 154, 155, 157, 158, 159, 161, 163, 165, 166, 167, 170, 173, 174, 177, 178, 179, 181, 182, 183, 185, 186, 187, 190, 191, 193, 194, 195, 197, 199, 201, 202, 203, 205, 206, 209, 210, 211, 213, 214, 215, 217, 218, 219, 221, 222, 223, 226, 227, 229, 230, 231, 233, 235, 237, 238, 239, 241, 246, 247, 249, 251, 253, 254, 255, 257, 258, 259, 262, 263, 265, 266, 267, 269, 271, 273, 274, 277, 278, 281, 282, 283, 285, 286, 287, 290, 291, 293, 295, 298, 299, 301, 302, 303, 305, 307, 309, 310, 311, 313, 314, 317, 318, 319, 321, 322, 323, 326, 327, 329, 330, 331, 334, 335, 337, 339, 341, 345, 346, 347, 349, 353, 354, 355, 357, 358, 359, 362, 365, 366, 367, 370, 371, 373, 374, 377, 379, 381, 382, 383, 385, 386, 389, 390, 391, 393, 394, 395, 397, 398, 399, 401, 402, 403, 406, 407, 409, 410, 411, 413, 415, 417, 418, 419, 421, 422, 426, 427, 429, 430, 431, 433, 434, 435, 437, 438, 439, 442, 443, 445, 446, 447, 449, 451, 453, 454, 455, 457, 458, 461, 462, 463, 465, 466, 467, 469, 470, 471, 473, 474, 478, 479, 481, 482, 483, 485, 487, 489, 491, 493, 494, 497, 498, 499, …

Cubefree numbers: 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113, 114, 115, 116, 117, 118, 119, 121, 122, 123, 124, 126, 127, 129, 130, 131, 132, 133, 134, 137, 138, 139, 140, 141, 142, 143, 145, 146, 147, 148, 149, 150, 151, 153, 154, 155, 156, 157, 158, 159, 161, 163, 164, 165, 166, 167, 169, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 181, 182, 183, 185, 186, 187, 188, 190, 191, 193, 194, 195, 196, 197, 198, 199, 201, 202, 203, 204, 205, 206, 207, 209, 210, 211, 212, 213, 214, 215, 217, 218, 219, 220, 221, 222, 223, 225, 226, 227, 228, 229, 230, 231, 233, 234, 235, 236, 237, 238, 239, 241, 242, 244, 245, 246, 247, 249, 251, 252, 253, 254, 255, 257, 258, 259, 260, 261, 262, 263, 265, 266, 267, 268, 269, 271, 273, 274, 275, 276, 277, 278, 279, 281, 282, 283, 284, 285, 286, 287, 289, 290, 291, 292, 293, 294, 295, 298, 299, 300, 301, 302, 303, 305, 306, 307, 308, 309, 310, 311, 313, 314, 315, 316, 317, 318, 319, 321, 322, 323, 325, 326, 327, 329, 330, 331, 332, 333, 334, 335, 337, 338, 339, 340, 341, 342, 345, 346, 347, 348, 349, 350, 353, 354, 355, 356, 357, 358, 359, 361, 362, 363, 364, 365, 366, 367, 369, 370, 371, 372, 373, 374, 377, 379, 380, 381, 382, 383, 385, 386, 387, 388, 389, 390, 391, 393, 394, 395, 396, 397, 398, 399, 401, 402, 403, 404, 406, 407, 409, 410, 411, 412, 413, 414, 415, 417, 418, 419, 420, 421, 422, 423, 425, 426, 427, 428, 429, 430, 431, 433, 434, 435, 436, 437, 438, 439, 441, 442, 443, 444, 445, 446, 447, 449, 450, 451, 452, 453, 454, 455, 457, 458, 460, 461, 462, 463, 465, 466, 467, 468, 469, 470, 471, 473, 474, 475, 476, 477, 478, 479, 481, 482, 483, 484, 485, 487, 489, 490, 491, 492, 493, 494, 495, 497, 498, 499, …

## Generated from a sieve

Lucky numbers: 1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99, 105, 111, 115, 127, 129, 133, 135, 141, 151, 159, 163, 169, 171, 189, 193, 195, 201, 205, 211, 219, 223, 231, 235, 237, 241, 259, 261, 267, 273, 283, 285, 289, 297, 303, 307, 319, 321, 327, 331, 339, 349, 357, 361, 367, 385, 391, 393, 399, 409, 415, 421, 427, 429, 433, 451, 463, 475, 477, 483, 487, 489, 495, 511, 517, 519, 529, 535, 537, 541, 553, 559, 577, 579, 583, 591, 601, 613, 615, 619, 621, 631, 639, 643, 645, 651, 655, 673, 679, 685, 693, 699, 717, 723, 727, 729, 735, 739, 741, 745, 769, 777, 781, 787, 801, 805, 819, 823, 831, 841, 855, 867, 873, 883, 885, 895, 897, 903, 925, 927, 931, 933, 937, 957, 961, 975, 979, 981, 991, 993, 997, 1009, 1011, 1021, 1023, 1029, 1039, 1041, 1053, 1057, 1087, 1093, 1095, 1101, 1105, 1107, 1117, 1123, 1147, 1155, 1167, 1179, 1183, 1189, 1197, 1201, 1203, 1209, 1219, 1231, 1233, 1245, 1249, 1251, 1261, 1263, 1275, 1281, 1285, 1291, 1303, 1309, 1323, 1329, 1339, 1357, 1365, 1369, 1387, 1389, 1395, 1401, 1417, 1419, 1435, 1441, 1455, 1459, 1471, 1473, 1485, 1491, 1495, 1497, 1501, 1503, 1519, 1533, 1543, 1545, 1563, 1567, 1575, 1579, 1585, 1587, 1597, 1599, 1611, 1639, 1641, 1645, 1659, 1663, 1675, 1693, 1701, 1705, 1711, 1723, 1731, 1737, 1749, 1765, 1767, 1771, 1773, 1777, 1797, 1801, 1809, 1819, 1827, 1831, 1833, 1839, 1857, 1869, 1879, 1893, 1899, 1915, 1921, 1923, 1933, 1941, 1945, 1959, 1963, 1965, 1977, 1983, 1987, 1995, …

Lucky primes: 3, 7, 13, 31, 37, 43, 67, 73, 79, 127, 151, 163, 193, 211, 223, 241, 283, 307, 331, 349, 367, 409, 421, 433, 463, 487, 541, 577, 601, 613, 619, 631, 643, 673, 727, 739, 769, 787, 823, 883, 937, 991, 997, 1009, 1021, 1039, 1087, 1093, 1117, 1123, 1201, 1231, 1249, 1291, 1303, 1459, 1471, 1543, 1567, 1579, 1597, 1663, 1693, 1723, 1777, 1801, 1831, 1879, 1933, 1987, 2053, 2083, 2113, 2221, 2239, 2251, 2281, 2311, 2467, 2473, 2557, 2593, 2647, 2671, 2689, 2797, 2851, 2887, 2953, 2971, 3037, 3049, 3109, 3121, 3163, 3187, 3229, 3259, 3301, 3307, 3313, 3433, 3499, 3559, 3571, 3607, 3613, 3697, 3709, 3727, 3793, 3847, 3889, 3931, 3943, 4003, 4129, 4201, 4363, 4441, 4483, 4519, 4561, 4567, 4621, 4663, 4801, 4813, 4951, 4969, 4987, 4993, 4999, 5179, 5233, 5419, 5449, 5503, 5527, 5569, 5641, 5701, 5737, 5827, 5839, 5851, 5869, 5923, 6079, 6163, 6211, 6229, 6271, 6301, 6367, 6373, 6379, 6427, 6553, 6661, 6679, 6733, 6763, 6841, 6871, 6883, 7069, 7129, 7207, 7237, 7321, 7333, 7459, 7489, 7507, 7549, 7591, 7603, 7639, 7687, 7717, 7951, 7963, 8089, 8161, 8191, 8221, 8233, 8263, 8269, 8467, 8539, 8641, 8647, 8719, 9151, 9181, 9277, 9349, 9403, 9421, 9547, 9613, 9631, 9643, 9649, 9661, 9733, 9811, 9883, …

Ludic numbers: 1, 2, 3, 5, 7, 11, 13, 17, 23, 25, 29, 37, 41, 43, 47, 53, 61, 67, 71, 77, 83, 89, 91, 97, 107, 115, 119, 121, 127, 131, 143, 149, 157, 161, 173, 175, 179, 181, 193, 209, 211, 221, 223, 227, 233, 235, 239, 247, 257, 265, 277, 283, 287, 301, 307, 313, 329, 331, 337, 341, 353, 359, 361, 377, 383, 389, 397, 407, 415, 419, 421, 431, 433, 437, 445, 463, 467, 475, 481, 493, 497, 503, 509, 517, 527, 535, 541, 553, 565, 577, 581, 593, 595, 607, 613, 617, 625, 643, 647, 653, 659, 667, 673, 685, 691, 697, 703, 707, 727, 733, 749, 751, 757, 775, 787, 791, 797, 803, 805, 811, 835, 839, 841, 851, 853, 857, 863, 865, 881, 893, 913, 929, 931, 937, 941, 943, 959, 961, 967, 973, 991, 997, 1007, 1015, 1021, 1043, 1045, 1049, 1061, 1063, 1093, 1097, 1103, 1105, 1111, 1123, 1133, 1141, 1147, 1151, 1177, 1193, 1201, 1207, 1217, 1223, 1225, 1229, 1231, 1237, 1247, 1255, 1271, 1277, 1283, 1297, 1303, 1313, 1315, 1333, 1351, 1361, 1363, 1367, 1375, 1379, 1381, 1391, 1403, 1427, 1435, 1439, 1441, 1465, 1481, 1487, 1493, 1507, 1511, 1517, 1525, 1531, 1537, 1541, 1553, 1559, 1567, 1577, 1589, 1601, 1627, 1631, 1643, 1651, 1657, 1667, 1675, 1679, 1691, 1705, 1709, 1717, 1721, 1723, 1735, 1757, 1769, 1777, 1781, 1795, 1799, 1811, 1813, 1823, 1829, 1831, 1841, 1847, 1853, 1859, 1877, 1891, 1901, 1907, 1915, 1919, 1931, 1943, 1961, 1973, 1987, 1993, 1997, …

Ludic primes: 2, 3, 5, 7, 11, 13, 17, 23, 29, 37, 41, 43, 47, 53, 61, 67, 71, 83, 89, 97, 107, 127, 131, 149, 157, 173, 179, 181, 193, 211, 223, 227, 233, 239, 257, 277, 283, 307, 313, 331, 337, 353, 359, 383, 389, 397, 419, 421, 431, 433, 463, 467, 503, 509, 541, 577, 593, 607, 613, 617, 643, 647, 653, 659, 673, 691, 727, 733, 751, 757, 787, 797, 811, 839, 853, 857, 863, 881, 929, 937, 941, 967, 991, 997, 1021, 1049, 1061, 1063, 1093, 1097, 1103, 1123, 1151, 1193, 1201, 1217, 1223, 1229, 1231, 1237, 1277, 1283, 1297, 1303, 1361, 1367, 1381, 1427, 1439, 1481, 1487, 1493, 1511, 1531, 1553, 1559, 1567, 1601, 1627, 1657, 1667, 1709, 1721, 1723, 1777, 1811, 1823, 1831, 1847, 1877, 1901, 1907, 1931, 1973, 1987, 1993, 1997, …

## Prime patterns

Twin primes: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139), (149, 151), (179, 181), (191, 193), (197, 199), (227, 229), (239, 241), (269, 271), (281, 283), (311, 313), (347, 349), (419, 421), (431, 433), (461, 463), (521, 523), (569, 571), (599, 601), (617, 619), (641, 643), (659, 661), (809, 811), (821, 823), (827, 829), (857, 859), (881, 883), (1019, 1021), (1031, 1033), (1049, 1051), (1061, 1063), (1091, 1093), (1151, 1153), (1229, 1231), (1277, 1279), (1289, 1291), (1301, 1303), (1319, 1321), (1427, 1429), (1451, 1453), (1481, 1483), (1487, 1489), (1607, 1609), (1619, 1621), (1667, 1669), (1697, 1699), (1721, 1723), (1787, 1789), (1871, 1873), (1877, 1879), (1931, 1933), (1949, 1951), (1997, 1999), (2027, 2029), (2081, 2083), (2087, 2089), (2111, 2113), (2129, 2131), (2141, 2143), (2237, 2239), (2267, 2269), (2309, 2311), (2339, 2341), (2381, 2383), (2549, 2551), (2591, 2593), (2657, 2659), (2687, 2689), (2711, 2713), (2729, 2731), (2789, 2791), (2801, 2803), (2969, 2971), (2999, 3001), (3119, 3121), (3167, 3169), (3251, 3253), (3257, 3259), (3299, 3301), (3329, 3331), (3359, 3361), (3371, 3373), (3389, 3391), (3461, 3463), (3467, 3469), (3527, 3529), (3539, 3541), (3557, 3559), (3581, 3583), (3671, 3673), (3767, 3769), (3821, 3823), (3851, 3853), (3917, 3919), (3929, 3931), (4001, 4003), (4019, 4021), (4049, 4051), (4091, 4093), (4127, 4129), (4157, 4159), (4217, 4219), (4229, 4231), (4241, 4243), (4259, 4261), (4271, 4273), (4337, 4339), (4421, 4423), (4481, 4483), (4517, 4519), (4547, 4549), (4637, 4639), (4649, 4651), (4721, 4723), (4878, 4789), (4799, 4801), (4931, 4933), (4967, 4969), (5009, 5011), (5021, 5023), (5099, 5101), (5231, 5233), (5279, 5281), (5417, 5419), (5441, 5443), (5477, 5479), (5501, 5503), (5519, 5521), (5639, 5641), (5651, 5653), (5657, 5659), (5741, 5743), (5849, 5851), (5867, 5869), (5879, 5881), (6089, 6091), (6131, 6133), (6197, 6199), (6269, 6271), (6299, 6301), (6359, 6361), (6449, 6451), (6551, 6553), (6569, 6571), (6659, 6661), (6689, 6691), (6701, 6703), (6761, 6763), (6779, 6781), (6791, 6793), (6827, 6829), (6869, 6871), (6947, 6949), (6959, 6961), (7127, 7129), (7211, 7213), (7307, 7309), (7331, 7333), (7349, 7351), (7457, 7459), (7487, 7489), (7547, 7549), (7559, 7561), (7589, 7591), (7757, 7759), (7877, 7879), (7949, 7951), (8009, 8011), (8087, 8089), (8219, 8221), (8231, 8233), (8291, 8293), (8387, 8389), (8429, 8431), (8537, 8539), (8597, 8599), (8627, 8629), (8819, 8821), (8837, 8839), (8861, 8863), (8969, 8971), (8999, 9001), (9011, 9013), (9041, 9043), (9239, 9241), (9281, 9283), (9341, 9343), (9419, 9421), (9431, 9433), (9437, 9439), (9461, 9463), (9629, 9631), (9677, 9679), (9719, 9721), (9767, 9769), (9857, 9859), (9929, 9931), … (all twin prime pairs except (3, 5) and (5, 7) end with the digits (1, 3), (7, 9) or (9, 1))

Cousin primes: (3, 7),(7, 11), (13, 17), (19, 23), (37, 41), (43, 47), (67, 71), (79, 83), (97, 101), (103, 107), (109, 113), (127, 131), (163, 167), (193, 197), (223, 227), (229, 233), (277, 281), (307, 311), (313, 317), (349, 353), (379, 383), (397, 401), (439, 443), (457, 461), (463, 467), (487, 491), (499, 503), (613, 617), (643, 647), (673, 677), (739, 743), (757, 761), (769, 773), (823, 827), (853, 857), (859, 863), (877, 881), (883, 887), (907, 911), (937, 941), (967, 971), (1009, 1013), (1087, 1091), (1093, 1097), (1213, 1217), (1279, 1283), (1297, 1301), (1303, 1307), (1423, 1427), (1429, 1433), (1447, 1451), (1483, 1487), (1489, 1493), (1549, 1553), (1567, 1571), (1579, 1583), (1597, 1601), (1609, 1613), (1663, 1667), (1693, 1697), (1783, 1787), (1867, 1871), (1873, 1877), (1993, 1997), (1999, 2003), (2083, 2087), (2137, 2141), (2203, 2207),(2239, 2243), (2269, 2273), (2293, 2297), (2347, 2351), (2377, 2381), (2389, 2393), (2437, 2441), (2473, 2477), (2539, 2543), (2617, 2621), (2659, 2663), (2683, 2687), (2689, 2693), (2707, 2711), (2749, 2753), (2797, 2801), (2833, 2837), (2857, 2861), (2953, 2957), (3019, 3023), (3037, 3041), (3079, 3083), (3163, 3167), (3187, 3191), (3217, 3221), (3253, 3257), (3319, 3323), (3343, 3347), (3457, 3461), (3463, 3467), (3529, 3533), (3613, 3617), (3673, 3677), (3697, 3701), (3793, 3797), (3847, 3851), (3877, 3881), (3907, 3911), (3919, 3923), (3943, 3947), (4003, 4007), (4129, 4133), (4153, 4157), (4447, 4451), (4513, 4517), (4519, 4523), (4639, 4643), (4729, 4733), (4783, 4787), (4789, 4793), (4813, 4817), (4933, 4937), (4969, 4973), (4999, 5003), (5077, 5081), (5167, 5171), (5227, 5231), (5233, 5237), (5347, 5351), (5413, 5417), (5437, 5441), (5479, 5483), (5503, 5507), (5527, 5531), (5569, 5573), (5647, 5651), (5653, 5657), (5689, 5693), (5737, 5741), (5779, 5783), (5839, 5843), (5857, 5861), (5923, 5927), (6007, 6011), (6043, 6047), (6199, 6203), (6217, 6221), (6469, 6473), (6547, 6551), (6577, 6581), (6733, 6737), (6823, 6827), (6829, 6833), (6907, 6911), (6967, 6971), (6997, 7001), (7039, 7043), (7207, 7211), (7243, 7247), (7477, 7481), (7537, 7541), (7573, 7577), (7603, 7607), (7639, 7643), (7669, 7673), (7687, 7691), (7699, 7703), (7723, 7727), (7753, 7757), (7789, 7793), (7873, 7877), (7879, 7883), (7933, 7937), (8089, 8093), (8167, 8171), (8233, 8237), (8269, 8273), (8287, 8291), (8293, 8297), (8419, 9423), (8443, 8447), (8539, 8543), (8623, 8627), (8677, 8681), (8689, 8693), (8737, 8741), (8778, 8783), (8803, 8807), (8863, 8867), (8929, 8933), (9007, 9011), (9133, 9137), (9157, 9161), (9199, 9203), (9277, 9281), (9319, 9323), (9337, 9341), (9433, 9437), (9463, 9467), (9547, 9551), (9619, 9623), (9739, 9743), (9787, 9791), (9829, 9833), (9883, 9887), …

## Divisors of a number

Divisors of 10: 1, 2, 5, 10 (4 divisors)

Divisors of 20: 1, 2, 4, 5, 10, 20 (6 divisors)

Divisors of 30: 1, 2, 3, 5, 6, 10, 15, 30 (8 divisors)

Divisors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100 (9 divisors)

Divisors of 1000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000 (16 divisors)

Divisors of 10000 (104): 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 100, 1250, 2000, 2500, 5000, 10000 (25 divisors)

Divisors of 100000 (105): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 625, 800, 1000, 1250, 2000, 2500, 3125, 4000, 5000, 6250, 10000, 12500, 20000, 25000, 50000, 100000 (36 divisors)

Divisors of 1000000 (106): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 625, 800, 1000, 1250, 1600, 2000, 2500, 3125, 4000, 5000, 6250, 8000, 10000, 12500, 15625, 20000, 25000, 31250, 40000, 50000, 62500, 100000, 125000, 200000, 250000, 500000, 1000000 (49 divisors)

Divisors of 10000000000 (1010): 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 512, 625, 640, 800, 1000, 1024, 1250, 1280, 1600, 2000, 2500, 2560, 3125, 3200, 4000, 5000, 5120, 6250, 6400, 8000, 10000, 12500, 12800, 15625, 16000, 20000, 25000, 25600, 31250, 32000, 40000, 50000, 62500, 64000, 78125, 80000, 100000, 125000, 128000, 156250, 160000, 200000, 250000, 312500, 320000, 390625, 400000, 500000, 625000, 640000, 781250, 800000, 1000000, 1250000, 1562500, 1600000, 1953125, 2000000, 2500000, 3125000, 3200000, 3906250, 4000000, 5000000, 6250000, 7812500, 8000000, 9765625, 10000000, 12500000, 15625000, 16000000, 19531250, 20000000, 25000000, 31250000, 39062500, 40000000, 50000000, 62500000, 78125000, 80000000, 100000000, 125000000, 156250000, 200000000, 250000000, 312500000, 400000000, 500000000, 625000000, 1000000000, 1250000000, 2000000000, 2500000000, 5000000000, 10000000000 (121 divisors)

Divisors of 1020: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 512, 625, 640, 800, 1000, 1024, 1250, 1280, 1600, 2000, 2048, 2500, 2560, 3125, 3200, 4000, 4096, 5000, 5120, 6250, 6400, 8000, 8192, 10000, 10240, 12500, 12800, 15625, 16000, 16384, 20000, 20480, 25000, 25600, 31250, 32000, 32768, 40000, 40960, 50000, 51200, 62500, 64000, 65536, 78125, 80000, 81920, 100000, 102400, 125000, 128000, 131072, 156250, 160000, 163840, 200000, 204800, 250000, 256000, 262144, 312500, 320000, 327680, 390625, 400000, 409600, 500000, 512000, 524288, 625000, 640000, 655360, 781250, 800000, 819200, 1000000, 1024000, 1048576, 1250000, 1280000, 1310720, 1562500, 1600000, 1638400, 1953125, 2000000, 2048000, 2500000, 2560000, 2621440, 3125000, 3200000, 3276800, 3906250, 4000000, 4096000, 5000000, 5120000, 5242880, 6250000, 6400000, 6553600, 7812500, 8000000, 8192000, 9765625, 10000000, …, 10000000000000000000, 12500000000000000000, 20000000000000000000, 25000000000000000000, 50000000000000000000, 100000000000000000000 (441 divisors)

Divisors of 10100: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 512, 625, 640, 800, 1000, 1024, 1250, 1280, 1600, 2000, 2048, 2500, 2560, 3125, 3200, 4000, 4096, 5000, 5120, 6250, 6400, 8000, 8192, 10000, 10240, 12500, 12800, 15625, 16000, 16384, 20000, 20480, 25000, 25600, 31250, 32000, 32768, 40000, 40960, 50000, 51200, 62500, 64000, 65536, 78125, 80000, 81920, 100000, 102400, 125000, 128000, 131072, 156250, 160000, 163840, 200000, 204800, 250000, 256000, 262144, 312500, 320000, 327680, 390625, 400000, 409600, 500000, 512000, 524288, 625000, 640000, 655360, 781250, 800000, 819200, 1000000, 1024000, 1048576, 1250000, 1280000, 1310720, 1562500, 1600000, 1638400, 1953125, 2000000, 2048000, 2097152, 2500000, 2560000, 2621440, 3125000, 3200000, 3276800, 3906250, 4000000, 4096000, 4194304, 5000000, 5120000, 5242880, 6250000, 6400000, 6553600, 7812500, 8000000, 8192000, 8388608, 9765625, 10000000, 10240000, 10485760, 12500000, 12800000, 13107200, 15625000, 16000000, 16384000, 16777216, 19531250, 20000000, 20480000, 20971520, 25000000, 25600000, 26214400, 31250000, 32000000, 32768000, 33554432, 39062500, 40000000, 40960000, 41943040, 48828125, 50000000, 51200000, 52428800, 62500000, 64000000, 65536000, 67108864, 78125000, 80000000, 81920000, 83886080, 97656250, 100000000, 102400000, 104857600, 125000000, 128000000, 131072000, 134217728, 156250000, 160000000, 163840000, 167772160, 195312500, 200000000, 204800000, 209715200, 244140625, 250000000, 256000000, 262144000, 268435456, 312500000, 320000000, 327680000, 335544320, 390625000, 400000000, 409600000, 419430400, 488281250, 500000000, 512000000, 524288000, 536870912, 625000000, 640000000, 655360000, 671088640, 781250000, 800000000, 819200000, 838860800, 976562500, 1000000000, 1024000000, 1048576000, 1073741824, 1220703125, 1250000000, 1280000000, 1310720000, 1342177280, 1562500000, 1600000000, 1638400000, 1677721600, 1953125000, 2000000000, 2048000000, 2097152000, 2147483648, 2441406250, 2500000000, 2560000000, 2621440000, 2684354560, 3125000000, 3200000000, 3276800000, 3355443200, 3906250000, 4000000000, 4096000000, 4194304000, 4294967296, 4882812500, 5000000000, 5120000000, 5242880000, 5368709120, 6103515625, 6250000000, 6400000000, 6553600000, 6710886400, 7812500000, 8000000000, 8192000000, 8388608000, 8589934592, 9765625000, 10000000000, …, 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (10201 divisors)

Divisors of 10!: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 50, 54, 56, 60, 63, 64, 70, 72, 75, 80, 81, 84, 90, 96, 100, 105, 108, 112, 120, 126, 128, 135, 140, 144, 150, 160, 162, 168, 175, 180, 189, 192, 200, 210, 216, 224, 225, 240, 252, 256, 270, 280, 288, 300, 315, 320, 324, 336, 350, 360, 378, 384, 400, 405, 420, 432, 448, 450, 480, 504, 525, 540, 560, 567, 576, 600, 630, 640, 648, 672, 675, 700, 720, 756, 768, 800, 810, 840, 864, 896, 900, 945, 960, 1008, 1050, 1080, 1120, 1134, 1152, 1200, 1260, 1280, 1296, 1344, 1350, 1400, 1440, 1512, 1575, 1600, 1620, 1680, 1728, 1792, 1800, 1890, 1920, 2016, 2025, 2100, 2160, 2240, 2268, 2304, 2400, 2520, 2592, 2688, 2700, 2800, 2835, 2880, 3024, 3150, 3200, 3240, 3360, 3456, 3600, 3780, 3840, 4032, 4050, 4200, 4320, 4480, 4536, 4725, 4800, 5040, 5184, 5376, 5400, 5600, 5670, 5760, 6048, 6300, 6400, 6480, 6720, 6912, 7200, 7560, 8064, 8100, 8400, 8640, 8960, 9072, 9450, 9600, 10080, 10368, 10800, 11200, 11340, 11520, 12096, 12600, 12960, 13440, 14175, 14400, 15120, 16128, 16200, 16800, 17280, 18144, 18900, 19200, 20160, 20736, 21600, 22400, 22680, 24192, 25200, 25920, 26880, 28350, 28800, 30240, 32400, 33600, 34560, 36288, 37800, 40320, 43200, 44800, 45360, 48384, 50400, 51840, 56700, 57600, 60480, 64800, 67200, 72576, 75600, 80640, 86400, 90720, 100800, 103680, 113400, 120960, 129600, 134400, 145152, 151200, 172800, 181440, 201600, 226800, 241920, 259200, 302400, 362880, 403200, 453600, 518400, 604800, 725760, 907200, 1209600, 1814400, 3628800 (270 divisors)

Divisors of 20!: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 48, 49, 50, 51, 52, 54, 55, 56, 57, 60, 63, 64, 65, 66, 68, 70, 72, 75, 76, 77, 78, 80, 81, 84, 85, 88, 90, 91, 95, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 117, 119, 120, 125, 126, 128, 130, 132, 133, 135, 136, 140, 143, 144, 147, 150, 152, 153, 154, 156, 160, 162, 165, 168, 170, 171, 175, 176, 180, 182, 187, 189, 190, 192, 195, 196, 198, 200, 204, 208, 209, 210, 216, 220, 221, 224, 225, 228, 231, 234, 238, 240, 243, 245, 247, 250, 252, 255, 256, 260, 264, 266, 270, 272, 273, 275, 280, 285, 286, 288, 294, 297, 300, 304, 306, 308, 312, 315, 320, 323, 324, 325, 330, 336, 340, 342, 350, 351, 352, 357, 360, 364, 374, 375, 378, 380, 384, 385, 390, 392, 396, 399, 400, 405, 408, 416, 418, 420, 425, 429, 432, 440, 441, 442, 448, 450, 455, 456, 459, 462, 468, 475, 476, 480, 486, 490, 494, 495, 500, 504, 510, 512, 513, 520, 525, 528, 532, 539, 540, 544, 546, 550, 560, 561, 567, 570, 572, 576, 585, 588, 594, 595, 600, 608, 612, 616, 624, 625, 627, 630, 637, 640, 646, 648, 650, 660, 663, 665, 672, 675, 680, 684, 693, 700, 702, 704, 714, 715, 720, 728, 729, 735, 741, 748, 750, 756, 760, 765, 768, 770, 780, 784, 792, 798, 800, 810, 816, 819, 825, 832, 833, 836, 840, 850, 855, 858, 864, 875, 880, 882, 884, 891, 896, 900, 910, 912, 918, 924, 931, 935, 936, 945, 950, 952, 960, 969, 972, 975, 980, 988, 990, …, 608225502044160000, 810967336058880000, 1216451004088320000, 2432902008176640000 (41040 divisors)

## Multiples of a number

Multiples of 3: 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, …

Multiples of 4: 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, …

Multiples of 5: 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, …

Multiples of 6: 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300, …

Multiples of 7: 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252, 259, 266, 273, 280, 287, 294, 301, 308, 315, 322, 329, 336, 343, 350, …

Multiples of 8: 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400, …

Multiples of 9: 0, 9, 19, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297, 306, 315, 324, 333, 342, 351, 360, 369, 378, 387, 396, 405, 414, 423, 432, 441, 450, …

Multiples of 10: 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 320, 330, 340, 350, 360, 370, 380, 390, 400, 410, 420, 430, 440, 450, 460, 470, 480, 490, 500, …

Multiples of 11: 0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220, 231, 242, 253, 264, 275, 286, 297, 308, 319, 330, 341, 352, 363, 374, 385, 396, 407, 418, 429, 440, 451, 462, 473, 484, 495, 506, 517, 528, 539, 550, …

Multiples of 12: 0, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 324, 336, 348, 360, 372, 384, 396, 408, 420, 432, 444, 456, 468, 480, 492, 504, 516, 528, 540, 552, 564, 576, 588, 600, …

Multiples of 13: 0, 13, 26,39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221, 234, 247, 260, 273, 286, 299, 312, 325, 338, 351, 364, 377, 390, 403, 416, 429, 442, 455, 468, 481, 494, 507, 520, 533, 546, 559, 572, 585, 598, 611, 624, 637, 650, …

Multiples of 14: 0, 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238, 252, 266, 280, 294, 308, 322, 336, 350, 364, 378, 392, 406, 420, 434, 448, 462, 476, 490, 504, 518, 532, 546, 560, 574, 588, 602, 616, 630, 646, 658, 672, 686, 700, …

Multiples of 15: 0, 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, 735, 750, …

Multiples of 16: 0, 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 256, 272, 288, 304, 320, 336, 352, 368, 384, 400, 416, 432, 448, 464, 480, 496, 512, 528, 544, 560, 576, 592, 608, 624, 640, 656, 672, 688, 704, 720, 736, 752, 768, 784, 800, …

Multiples of 17: 0, 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 272, 289, 306, 323, 340, 357, 374, 391, 408, 425, 442, 459, 476, 493, 510, 527, 544, 561, 578, 595, 612, 629, 646, 663, 680, 697, 714, 731, 748, 765, 782, 799, 816, 833, 850, …

Multiples of 18: 0, 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, 270, 288, 306, 324, 342, 360, 378, 396, 414, 432, 450, 468, 486, 504, 522, 540, 558, 576, 594, 612, 630, 648, 666, 684, 702, 720, 738, 756, 774, 792, 810, 828, 846, 864, 882, 900, …

Multiples of 19: 0, 19, 38, 57, 76, 95, 114, 133, 152, 171, 190, 209, 228, 247, 266, 285, 304, 323, 342, 361, 380, 399, 418, 437, 456, 475, 494, 513, 532, 551, 570, 589, 608, 627, 646, 665, 684, 703, 722, 741, 760, 779, 798, 817, 836, 855, 874, 893, 912, 931, 950, …

Multiples of 20: 0, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300, 320, 340, 360, 380, 400, 420, 440, 460, 480, 500, 520, 540, 560, 580, 600, 620, 640, 660, 680, 700, 720, 740, 760, 780, 800, 820, 840, 860, 880, 900, 920, 940, 960, 980, 1000, …

## *n*th powers

Squares (or 2nd powers): 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 3025, 3136, 3249, 3364, 3481, 3600, 3721, 3844, 3969, 4096, 4225, 4356, 4489, 4624, 4761, 4900, 5041, 5184, 5329, 5476, 5625, 5776, 5929, 6084, 6241, 6400, 6561, 6724, 6889, 7056, 7225, 7396, 7569, 7744, 7921, 8100, 8281, 8464, 8649, 9025, 9216, 9409, 9604, 9801, 10000, 10201, 10404, 10609, 10816, 11025, 11236, 11449, 11664, 11881, 12100, 12321, 12544, 12769, 12996, 13225, 13456, 13689, 13924, 14161, 14400, 19881, 20164, 20449, 20736, 21025, 21316, 21609, 21904, 22201, 22500, 22801, 23104, 23409, 23716, 24025, 24336, 24649, 24964, 25281, 25600, 25921, 26244, 26569, 26896, 27225, 27556, 27889, 28224, 28561, 28900, 29241, 29584, 29929, 30276, 30625, 30976, 31329, 31684, 32041, 32400, 32761, 33124, 33489, 33856, 34225, 34596, 34969, 35344, 35721, 36100, 36481, 36864, 37249, 37636, 38025, 38416, 38809, 39204, 39601, 40000, … (all squares end with the digits 0, 1, 4, 5, 6 or 9)

Cubes (or 3rd powers, hexahedral numbers): 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 27000, 29791, 32768, 35937, 39304, 42875, 46656, 50653, 54872, 59319, 64000, 68921, 74088, 79507, 85184, 91125, 97336, 103823, 110592, 117649, 125000, 132651, 140608, 148877, 157464, 166375, 175616, 185193, 195112, 205379, 216000, 226981, 238328, 250047 262144 274625, 287496, 300763, 314432, 328509, 343000, 357911, 373248, 389017, 405224, 421875, 438976, 456533, 474552, 493039, 512000, 531441, 551368, 571787, 592704, 614125, 636056, 658503, 681472, 704969, 729000, 753571, 778688, 804357, 830584, 857375, 884736, 912673, 941192, 970299, 1000000, …

4th powers: 0, 1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 10000, 14641, 20736, 28561, 38416, 50625, 65536, 83521, 104976, 130321, 160000, 194481, 234256, 279841, 331776, 390625, 456976, 531441, 614656, 707281, 810000, 923521, 1048576, 1185921, 1336336, 1500625, 1679616, 1874161, 2085136, 2313441, 2560000, 2825761, 3111696, 3418801, 3748096, 4100625, 4477456, 4879681, 5308416, 5764801, 6250000, 6765201, 7311616, 7890481, 8503056, 9150625, 9834496, 10556001, 11316496, 12117361, 12960000, 13845841, 14776336, 15752961, 16777216, 17850625, 18974736, 20151121, 21381376, 22667121, 24010000, 25411681, 26873856, 28398241, 29986576, 31640625, 33362176, 35153041, 37015056, 38950081, 40960000, 43046721, 45212176, 47458321, 49787136, 52200625, 54700816, 57289761, 59969536, 62742241, 65610000, 68574961, 71639296, 74805201, 78074896, 81450625, 84934656, 88529281, 92236816, 96059601, 100000000, … (all 4th powers end with the digits 0, 1, 5 or 6)

5th powers: 0, 1, 32, 243, 1024, 3125, 7776, 16807, 32768, 59049, 100000, 161051, 248832, 371293, 537824, 759375, 1048576, 1419857, 1889568, 2476099, 3200000, 4084101, 5153632, 6436343, 7962624, 9765625, 11881376, 14348907, 17210368, 20511149, 24300000, 28629151, 33554432, 39135393, 45435424, 52521875, 60466176, 69343957, 79235168, 90224199, 102400000, 115856201, 130691232, 147008443, 164916224, 184528125, 205962976, 229345007, 254803968, 282475249, 312500000, 345025251, 380204032, 418195493, 459165024, 503284375, 550731776, 601692057, 656356768, 714924299, 777600000, 844596301, 916132832, 992436543, 1073741824, 1160290625, 1252332576, 1350125107, 1453933568, 1564031349, 1680700000, 1804229351, 1934917632, 2073071593, 2219006624, 2373046875, 2535525376, 2706784157, 2887174368, 3077056399, 3276800000, 3486784401, 3707398432, 3939040643, 4182119424, 4437053125, 4704270176, 4984209207, 5277319168, 5584059449, 5904900000, 6240321451, 6590815232, 6956883693, 7339040224, 7737809375, 8153726976, 8587340257, 9039207968, 9509900499, 10000000000, …

6th powers: 0, 1, 64, 729, 4096, 15625, 46656, 117649, 262144, 531441, 1000000, 1771561, 2985984, 4826809, 7529536, 11390625, 16777216, 24137569, 34012224, 47045881, 64000000, 85766121, 113379904, 148035889, 191102976, 244140625, 308915776, 387420489, 481890304, 594823321, 729000000, 887503681, 1073741824, 1291467969, 1544804416, 1838265625, 2176782336, 2565726409, 3010936384, 3518743761, 4096000000, 4750104241, 5489031744, 6321363049, 7256313856, 8303765625, 9474296896, 10779215329, 12230590464, 13841287201, 15625000000, …

7th powers: 0, 1, 128, 2187, 16384, 78125, 279936, 823543, 2097152, 4782969, 10000000, 19487171, 35831808, 62748517, 105413504, 170859375, 268435456, 410338673, 612220032, 893871739, 1280000000, 1801088541, 2494357888, 3404825447, 4586471424, 6103515625, 8031810176, 10460353203, 13492928512, 17249876309, 21870000000, 27512614111, 34359738368, 42618442977, 52523350144, 64339296875, 78364164096, 94931877133, 114415582592, 137231006679, 163840000000, 194754273881, 230539333248, 271818611107, 319277809664, 373669453125, 435817657216, 506623120463, 587068342272, 678223072849, 781250000000, …

8th powers: 0, 1, 256, 6561, 65536, 390625, 1679616, 5764801, 16777216, 43046721, 100000000, 214358881, 429981696, 815730721, 1475789056, 2562890625, 4294967296, 6975757441, 11019960576, 16983563041, 25600000000, 37822859361, 54875873536, 78310985281, 110075314176, 152587890625, 208827064576, 282429536481, 377801998336, 500246412961, 656100000000, 852891037441, 1099511627776, 1406408618241, 1785793904896, 2251875390625, 2821109907456, 3512479453921, 4347792138496, 5352009260481, 6553600000000, 7984925229121, 9682651996416, 11688200277601, 14048223625216, 16815125390625, 20047612231936, 23811286661761, 28179280429056, 33232930569601, 39062500000000, …

9th powers: 0, 1, 512, 19683, 262144, 1953125, 10077696, 40353607, 134217728, 387420489, 1000000000, 2357947691, 5159780352, 10604499373, 20661046784, 38443359375, 68719476736, 118587876497, 198359290368, 322687697779, 512000000000, 794280046581, 1207269217792, 1801152661463, 2641807540224, 3814697265625, 5429503678976, 7625597484987, 10578455953408, 14507145975869, 19683000000000, 26439622160671, 35184372088832, 46411484401953, 60716992766464, 78815638671875, 101559956668416, 129961739795077, 165216101262848, 208728361158759, 262144000000000, 327381934393961, 406671383849472, 502592611936843, 618121839509504, 756680642578125, 922190162669056, 1119130473102767, 1352605460594688, 1628413597910449, 1953125000000000, …

10th powers: 0, 1, 1024, 59049, 1048576, 9765625, 60466176, 282475249, 1073741824, 3486784401, 10000000000, 25937424601, 61917364224, 137858491849, 289254654976, 576650390625, 1099511627776, 2015993900449, 3570467226624, 6131066257801, 10240000000000, 16679880978201, 26559922791424, 41426511213649, 63403380965376, 95367431640625, 141167095653376, 205891132094649, 296196766695424, 420707233300201, 590490000000000, 819628286980801, 1125899906842624, 1531578985264449, 2064377754059776, 2758547353515625, 3656158440062976, 4808584372417849, 6278211847988224, 8140406085191601, 10485760000000000, 13422659310152401, 17080198121677824, 21611482313284249, 27197360938418176, 34050628916015625, 42420747482776576, 52599132235830049, 64925062108545024, 79792266297612001, 97656250000000000, …

11th powers: 0, 1, 2048, 177147, 4194304, 48828125, 362797056, 1977326743, 8589934592, 31381059609, 100000000000, 285311670611, 743008370688, 1792160394037, 4049565169664, 8649755859375, 17592186044416, 34271896307633, 64268410079232, 116490258898219, 204800000000000, 350277500542221, 584318301411328, 952809757913927, 1521681143169024, 2384185791015625, 3670344486987776, 5559060566555523, 8293509467471872, 12200509765705829, 17714700000000000, 25408476896404831, 36028797018963968, 50542106513726817, 70188843638032384, 96549157373046875, 131621703842267136, 177917621779460413, 238572050223552512, 317475837322472439, 419430400000000000, 550329031716248441, 717368321110468608, 929293739471222707, 1196683881290399744, 1532278301220703125, 1951354384207722496, 2472159215084012303, 3116402981210161152, 3909821048582988049, 4882812500000000000, …

12th powers: 0, 1, 4096, 531441, 16777216, 244140625, 2176782336, 13841287201, 68719476736, 282429536481, 1000000000000, 3138428376721, 8916100448256, 23298085122481, 56693912375296, 129746337890625, 281474976710656, 582622237229761, 1156831381426176, 2213314919066161, 4096000000000000, 7355827511386641, 12855002631049216, 21914624432020321, 36520347436056576, 59604644775390625, 95428956661682176, 150094635296999121, 232218265089212416, 353814783205469041, 531441000000000000, 787662783788549761, 1152921504606846976, 1667889514952984961, 2386420683693101056, 3379220508056640625, 4738381338321616896, 6582952005840035281, 9065737908494995456, 12381557655576425121, 16777216000000000000, 22563490300366186081, 30129469486639681536, 39959630797262576401, 52654090776777588736, 68952523554931640625, 89762301673555234816, 116191483108948578241, 149587343098087735296, 191581231380566414401, 244140625000000000000, …

13th powers: 0, 1, 8192, 1594323, 67108864, 1220703125, 13060694016, 96889010407, 549755813888, 2541865828329, 10000000000000, 34522712143931, 106993205379072, 302875106592253, 793714773254144, 1946195068359375, 4503599627370496, 9904578032905937, 20822964865671168, 42052983462257059, 81920000000000000, 154472377739119461, 282810057883082752, 504036361936467383, 876488338465357824, 1490116119384765625, 2481152873203736576, 4052555153018976267, 6502111422497947648, 10260628712958602189, 15943230000000000000, 24417546297445042591, 36893488147419103232, 55040353993448503713, 81138303245565435904, 118272717781982421875, 170581728179578208256, 243569224216081305397, 344498040522809827328, 482880748567480579719, 671088640000000000000, 925103102315013629321, 1265437718438866624512, 1718264124282290785243, 2316779994178213904384, 3102863559971923828125, 4129065876983540801536, 5460999706120583177327, 7180192468708211294208, 9387480337647754305649, 12207031250000000000000, …

14th powers: 0, 1, 16384, 4782969, 268435456, 6103515625, 78364164096, 678223072849, 4398046511104, 22876792454961, 100000000000000, 379749833583241, 1283918464548864, 3937376385699289, 11112006825558016, 29192926025390625, 72057594037927936, 168377826559400929, 374813367582081024, 799006685782884121, 1638400000000000000, 3243919932521508681, 6221821273427820544, 11592836324538749809, 21035720123168587776, 37252902984619140625, 64509974703297150976, 109418989131512359209, 182059119829942534144, 297558232675799463481, 478296900000000000000, 756943935220796320321, 1180591620717411303424, 1816331681783800622529, 2758702310349224820736, 4139545122369384765625, 6140942214464815497216, 9012061295995008299689, 13090925539866773438464, 18832349194131742609041, 26843545600000000000000, 37929227194915558802161, 53148384174432398229504, 73885357344138503765449, 101938319743841411792896, 139628860198736572265625, 189937030341242876870656, 256666986187667409334369, 344649238497994142121984, 459986536544739960976801, 610351562500000000000000, …

15th powers: 0, 1, 32768, 14348907, 1073741824, 30517578125, 470184984576, 4747561509943, 35184372088832, 205891132094649, 1000000000000000, 4177248169415651, 15407021574586368, 51185893014090757, 155568095557812224, 437893890380859375, 1152921504606846976, 2862423051509815793, 6746640616477458432, 15181127029874798299, 32768000000000000000, 68122318582951682301, 136880068015412051968, 266635235464391245607, 504857282956046106624, 931322574615478515625, 1677259342285725925376, 2954312706550833698643, 5097655355238390956032, 8629188747598184440949, 14348907000000000000000, 23465261991844685929951, 37778931862957161709568, 59938945498865420543457, 93795878551873643905024, 144884079282928466796875, 221073919720733357899776, 333446267951815307088493, 497455170514937390661632, 734461618571137961752599, 1073741824000000000000000, 1555098314991537910888601, 2232232135326160725639168, 3177070365797955661914307, 4485286068729022118887424, 6283298708943145751953125, 8737103395697172336050176, 12063348350820368238715343, 16543163447903718821855232, 22539340290692258087863249, 30517578125000000000000000, …

16th powers: 0, 1, 65536, 43046721, 4294967296, 152587890625, 2821109907456, 33232930569601, 281474976710656, 1853020188851841, 10000000000000000, 45949729863572161, 184884258895036416, 665416609183179841, 2177953337809371136, 6568408355712890625, 18446744073709551616, 48661191875666868481, 121439531096594251776, 288441413567621167681, 655360000000000000000, 1430568690241985328321, 3011361496339065143296, 6132610415680998648961, 12116574790945106558976, 23283064365386962890625, 43608742899428874059776, 79766443076872509863361, 142734349946674946768896, 250246473680347348787521, 430467210000000000000000, 727423121747185263828481, 1208925819614629174706176, 1977985201462558877934081, 3189059870763703892770816, 5070942774902496337890625, 7958661109946400884391936, 12337511914217166362274241, 18903296479567620845142016, 28644003124274380508351361, 42949672960000000000000000, 63759030914653054346432641, 93753749683698750476845056, 136614025729312093462315201, 197352587024076973231046656, 282748441902441558837890625, 401906756202069927458308096, 566977372488557307219621121, 794071845499378503449051136, 1104427674243920646305299201, 1525878906250000000000000000, …

17th powers: 0, 1, 131072, 129140163, 17179869184, 762939453125, 16926659444736, 232630513987207, 2251799813685248, 16677181699666569, 100000000000000000, 505447028499293771, 2218611106740436992, 8650415919381337933, 30491346729331195904, 98526125335693359375, 295147905179352825856, 827240261886336764177, 2185911559738696531968, 5480386857784802185939, 13107200000000000000000, 30041942495081691894741, 66249952919459433152512, 141050039560662968926103, 290797794982682557415424, 582076609134674072265625, 1133827315385150725554176, 2153693963075557766310747, 3996561798506898509529088, 7257147736730073114838109, 12914016300000000000000000, 22550116774162743178682911, 38685626227668133590597632, 65273511648264442971824673, 108428035605965932354207744, 177482997121587371826171875, 286511799958070431838109696, 456487940826035155404146917, 718325266223569592115396608, 1117116121846700839825703079, 1717986918400000000000000000, 2614120267500775228203738281, 3937657486715347520027492352, 5874403106360420018879553643, 8683513829059386822166052864, 12723679885609870147705078125, 18487710785295216663082172416, 26647936506962193439322192687, 38115448583970168165554454528, 54116956037952111668959660849, 76293945312500000000000000000, …

18th powers: 0, 1, 262144, 387420489, 68719476736, 3814697265625, 101559956668416, 1628413597910449, 18014398509481984, 150094635296999121, 1000000000000000000, 5559917313492231481, 26623333280885243904, 112455406951957393129, 426878854210636742656, 1477891880035400390625, 4722366482869645213696, 14063084452067724991009, 39346408075296537575424, 104127350297911241532841, 262144000000000000000000, 630880792396715529789561, 1457498964228107529355264, 3244150909895248285300369, 6979147079584381377970176, 14551915228366851806640625, 29479510200013918864408576, 58149737003040059690390169, 111903730358193158266814464, 210457284365172120330305161, 387420489000000000000000000, 699053619999045038539170241, 1237940039285380274899124224, 2154025884392726618070214209, 3686553210602841700043063296, 6211904899255558013916015625, 10314424798490535546171949056, 16890053810563300749953435929, 27296360116495644500385071104, 43567528752021332753202420081, 68719476736000000000000000000, 107178930967531784356353269521, 165381614442044595841154678784, 252599333573498060811820806649, 382074608478613020175306326016, 572565594852444156646728515625, 850434696123579966501779931136, 1252453015827223091648143056289, 1829541532030568071946613817344, 2651730845859653471779023381601, 3814697265625000000000000000000, …

19th powers: 0, 1, 524288, 1162261467, 274877906944, 19073486328125, 609359740010496, 11398895185373143, 144115188075855872, 1350851717672992089, 10000000000000000000, 61159090448414546291, 319479999370622926848, 1461920290375446110677, 5976303958948914397184, 22168378200531005859375, 75557863725914323419136, 239072435685151324847153, 708235345355337676357632, 1978419655660313589123979, 5242880000000000000000000, 13248496640331026125580781, 32064977213018365645815808, 74615470927590710561908487, 167499529910025153071284224, 363797880709171295166015625, 766467265200361890474622976, 1570042899082081611640534563, 3133304450029408431470804992, 6103261246589991489578849669, 11622614670000000000000000000, 21670662219970396194714277471, 39614081257132168796771975168, 71082854184959978396317068897, 125342809160496617801464152064, 217416671473944530487060546875, 371319292745659279662190166016, 624931990990842127748277129373, 1037261684426834491014632701952, 1699133621328831977374894383159, 2748779069440000000000000000000, 4394336169668803158610484050361, 6946027806565873025328496508928, 10861771343660416614908294685907, 16811282773058972887713478344704, 25765451768359987049102783203125, 39119996021684678459081876832256, 58865291743879485307462723645583, 87817993537467267453437463232512, 129934811447123020117172145698449, 190734863281250000000000000000000, …

20th powers: 0, 1, 1048576, 3486784401, 1099511627776, 95367431640625, 3656158440062976, 79792266297612001, 1152921504606846976, 12157665459056928801, 100000000000000000000, 672749994932560009201, 3833759992447475122176, 19004963774880799438801, 83668255425284801560576, 332525673007965087890625, 1208925819614629174706176, 4064231406647572522401601, 12748236216396078174437376, 37589973457545958193355601, 104857600000000000000000000, 278218429446951548637196401, 705429498686404044207947776, 1716155831334586342923895201, 4019988717840603673710821376, 9094947017729282379150390625, 19928148895209409152340197376, 42391158275216203514294433201, 87732524600823436081182539776, 176994576151109753197786640401, 348678440100000000000000000000, 671790528819082282036142601601, 1267650600228229401496703205376, 2345734188103679287078463273601, 4261655511456885005249781170176, 7609583501588058567047119140625, 23122483666661158726686253786801, 39415944008219710658556042674176, 66266211231824447117620880943201, 109951162777600000000000000000000, 180167782956420929503029846064801, 291733167875766667063796853374976, 467056167777397914441056671494001, 739696442014594807059393047166976, 1159445329576199417209625244140625, 1799519816997495209117766334283776, 2766668711962335809450748011342401, 4215263689798428837764998235160576, 6366805760909027985741435139224001, 9536743164062500000000000000000000, …

## Powers of a number

Powers of 2 (or 2-smooth numbers): 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592, 17179869184, 34359738368, 68719476736, 137438953472, 274877906944, 549755813888, 1099511627776, 2199023255552, 4398046511104, 8796093022208, 17592186044416, 35184372088832, 70368744177664, 140737488355328, 281474976710656, 562949953421312, 1125899906842624, 2251799813685248, 4503599627370496, 9007199254740992, 18014398509481984, 36028797018963968, 72057594037927936, 144115188075855872, 288230376151711744, 576460752303423488, 1152921504606846976, 2305843009213693952, 4611686018427387904, 9223372036854775808, 18446744073709551616, 36893488147419103232, 73786976294838206464, 147573952589676412928, 295147905179352825856, 590295810358705651712, 1180591620717411303424, 2361183241434822606848, 4722366482869645213696, 9444732965739290427392, 18889465931478580854784, 37778931862957161709568, 75557863725914323419136, 151115727451828646838272, 302231454903657293676544, 604462909807314587353088, 1208925819614629174706176, 2417851639229258349412352, 4835703278458516698824704, 9671406556917033397649408, 19342813113834066795298816, 38685626227668133590597632, 77371252455336267181195264, 154742504910672534362390528, 309485009821345068724781056, 618970019642690137449562112, 1237940039285380274899124224, 2475880078570760549798248448, 4951760157141521099596496896, 9903520314283042199192993792, 19807040628566084398385987584, 39614081257132168796771975168, 79228162514264337593543950336, 158456325028528675187087900672, 316912650057057350374175801344, 633825300114114700748351602688, 1267650600228229401496703205376, … (all powers of 2 except 1 end with the digits 2, 4, 6 or 8; except for 1 and 2, the last two digits repeat in a cycle of 20: 04, 08, 16, 32, 64, 28, 56, 12, 24, 48, 96, 92, 84, 68, 36, 72, 44, 88, 76, 52)

Powers of 3: 1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 129140163, 387420489, 1162261467, 3486784401, 10460353203, 31381059609, 94143178827, 282429536481, 847288609443, 2541865828329, 7625597484987, 22876792454961, 68630377364883, 205891132094649, 617673396283947, 1853020188851841, 5559060566555523, 16677181699666569, 50031545098999707, 150094635296999121, 450283905890997363, 1350851717672992089, 4052555153018976267, 12157665459056928801, 36472996377170786403, 109418989131512359209, 328256967394537077627, 984770902183611232881, 2954312706550833698643, 8862938119652501095929, 26588814358957503287787, 79766443076872509863361, 239299329230617529590083, 717897987691852588770249, 2153693963075557766310747, 6461081889226673298932241, 19383245667680019896796723, 58149737003040059690390169, 174449211009120179071170507, 523347633027360537213511521, 1570042899082081611640534563, 4710128697246244834921603689, 14130386091738734504764811067, 42391158275216203514294433201, 127173474825648610542883299603, 381520424476945831628649898809, 1144561273430837494885949696427, 3433683820292512484657849089281, 10301051460877537453973547267843, 30903154382632612361920641803529, 92709463147897837085761925410587, 278128389443693511257285776231761, 834385168331080533771857328695283, 2503155504993241601315571986085849, 7509466514979724803946715958257547, 22528399544939174411840147874772641, 67585198634817523235520443624317923, 202755595904452569706561330872953769, 608266787713357709119683992618861307, 1824800363140073127359051977856583921, 5474401089420219382077155933569751763, 16423203268260658146231467800709255289, 49269609804781974438694403402127765867, 147808829414345923316083210206383297601, 443426488243037769948249630619149892803, 1330279464729113309844748891857449678409, 3990838394187339929534246675572349035227, 11972515182562019788602740026717047105681, 35917545547686059365808220080151141317043, 107752636643058178097424660240453423951129, 323257909929174534292273980721360271853387, 969773729787523602876821942164080815560161, 2909321189362570808630465826492242446680483, 8727963568087712425891397479476727340041449, 26183890704263137277674192438430182020124347, 78551672112789411833022577315290546060373041, 235655016338368235499067731945871638181119123, 706965049015104706497203195837614914543357369, 2120895147045314119491609587512844743630072107, 6362685441135942358474828762538534230890216321, 19088056323407827075424486287615602692670648963, 57264168970223481226273458862846808078011946889, 171792506910670443678820376588540424234035840667, 515377520732011331036461129765621272702107522001, … (all powers of 3 end with the digits 1, 3, 7 or 9; the last two digits repeat in a cycle of 20: 01, 03, 09, 27, 81, 43, 29, 87, 61, 83, 49, 47, 41, 23, 69, 07, 21, 63, 89, 67)

Powers of 4: 1, 4, 16, 64, 256, 1024, 4096, 16384, 65536, 262144, 1048576, 4194304, 16777216, 67108864, 268435456, 1073741824, 4294967296, 17179869184, 68719476736, 274877906944, 1099511627776, 4398046511104, 17592186044416, 70368744177664, 281474976710656, 1125899906842624, 4503599627370496, 18014398509481984, 72057594037927936, 288230376151711744, 1152921504606846976, 4611686018427387904, 18446744073709551616, 73786976294838206464, 295147905179352825856, 1180591620717411303424, 4722366482869645213696, 18889465931478580854784, 75557863725914323419136, 302231454903657293676544, 1208925819614629174706176, 4835703278458516698824704, 19342813113834066795298816, 77371252455336267181195264, 309485009821345068724781056, 1237940039285380274899124224, 4951760157141521099596496896, 19807040628566084398385987584, 79228162514264337593543950336, 316912650057057350374175801344, 1267650600228229401496703205376, …

Powers of 5: 1, 5, 25, 125, 625, 3125, 15625, 78125, 390625, 1953125, 9765625, 48828125, 244140625, 1220703125, 6103515625, 30517578125, 152587890625, 762939453125, 3814697265625, 19073486328125, 95367431640625, 476837158203125, 2384185791015625, 11920928955078125, 59604644775390625, 298023223876953125, 1490116119384765625, 7450580596923828125, 37252902984619140625, 186264514923095703125, 931322574615478515625, 4656612873077392578125, 23283064365386962890625, 116415321826934814453125, 582076609134674072265625, 2910383045673370361328125, 14551915228366851806640625, 72759576141834259033203125, 363797880709171295166015625, 1818989403545856475830078125, 9094947017729282379150390625, 45474735088646411895751953125, 227373675443232059478759765625, 1136868377216160297393798828125, 5684341886080801486968994140625, 28421709430404007434844970703125, 142108547152020037174224853515625, 710542735760100185871124267578125, 3552713678800500929355621337890625, 17763568394002504646778106689453125, 88817841970012523233890533447265625, …

Powers of 6: 1, 6, 36, 216, 1296, 7776, 46656, 279936, 1679616, 10077696, 60466176, 362797056, 2176782336, 13060694016, 78364164096, 470184984576, 2821109907456, 16926659444736, 101559956668416, 609359740010496, 3656158440062976, 21936950640377856, 131621703842267136, 789730223053602816, 4738381338321616896, 28430288029929701376, 170581728179578208256, 1023490369077469249536, 6140942214464815497216, 36845653286788892983296, 221073919720733357899776, 1326443518324400147398656, 7958661109946400884391936, 47751966659678405306351616, 286511799958070431838109696, 1719070799748422591028658176, 10314424798490535546171949056, 61886548790943213277031694336, 371319292745659279662190166016, 2227915756473955677973140996096, 13367494538843734067838845976576, 80204967233062404407033075859456, 481229803398374426442198455156736, 2887378820390246558653190730940416, 17324272922341479351919144385642496, 103945637534048876111514866313854976, 623673825204293256669089197883129856, 3742042951225759540014535187298779136, 22452257707354557240087211123792674816, 134713546244127343440523266742756048896, 808281277464764060643139600456536293376, …

Powers of 7: 1, 7, 49, 343, 2401, 16807, 117649, 823543, 5764801, 40353607, 282475249, 1977326743, 13841287201, 96889010407, 678223072849, 4747561509943, 33232930569601, 232630513987207, 1628413597910449, 11398895185373143, 79792266297612001, 558545864083284007, 3909821048582988049, 27368747340080916343, 191581231380566414401, 1341068619663964900807, …

Powers of 8: 1, 8, 64, 512, 4096, 32768, 262144, 2097152, 16777216, 134217728, 1073741824, 8589934592, 68719476736, 549755813888, 4398046511104, 35184372088832, 281474976710656, 2251799813685248, 18014398509481984, 144115188075855872, 1152921504606846976, 9223372036854775808, 73786976294838206464, 590295810358705651712, 4722366482869645213696,37778931862957161709568, …

Powers of 9: 1, 9, 81, 729, 6561, 59049, 531441, 4782969, 43046721, 387420489, 3486784401, 31381059609, 282429536481, 2541865828329, 22876792454961, 205891132094649, 1853020188851841, 16677181699666569, 150094635296999121, 1350851717672992089, 12157665459056928801, 109418989131512359209, 984770902183611232881, 8862938119652501095929, 79766443076872509863361, 717897987691852588770249, …

Powers of 10: 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 10000000000000000, 100000000000000000, 1000000000000000000, 10000000000000000000, 100000000000000000000, 1000000000000000000000, 10000000000000000000000, 100000000000000000000000, 1000000000000000000000000, 10000000000000000000000000, …

Powers of 11: 1, 11, 121, 1331, 14641, 161051, 1771561, 19487171, 214358881, 2357947691, 25937424601, 285311670611, 3138428376721, 34522712143931, 379749833583241, 4177248169415651, 45949729863572161, 505447028499293771, 5559917313492231481, 61159090448414546291, 672749994932560009201, 7400249944258160101211, 81402749386839761113321, 895430243255237372246531, 9849732675807611094711841, 108347059433883722041830251, … (the powers of 11 up to 114 gives the digits of the *n*th row of the Pascal's triangle, from 115 onwards, the digits overlap)

Powers of 12: 1, 12, 144, 1728, 20736, 248832, 2985984, 35831808, 429981696, 5159780352, 61917364224, 743008370688, 8916100448256, 106993205379072, 1283918464548864, 15407021574586368, 184884258895036416, 2218611106740436992, 26623333280885243904, 319479999370622926848, 3833759992447475122176, 46005119909369701466112, 552061438912436417593344, 6624737266949237011120128, 79496847203390844133441536, 953962166440690129601298432, …

Powers of 13: 1, 13, 169, 2197, 28561, 371293, 4826809, 62748517, 815730721, 10604499373, 137858491849, 1792160394037, 23298085122481, 302875106592253, 3937376385699289, 51185893014090757, 665416609183179841, 8650415919381337933, 112455406951957393129, 1461920290375446110677, 19004963774880799438801, 247064529073450392704413, 3211838877954855105157369, 41753905413413116367045797, 542800770374370512771595361, 7056410014866816666030739693, …

Powers of 14: 1, 14, 196, 2744, 38416, 537824, 7529536, 105413504, 1475789056, 20661046784, 289254654976, 4049565169664, 56693912375296, 793714773254144, 11112006825558016, 155568095557812224, 2177953337809371136, 30491346729331195904, 426878854210636742656, 5976303958948914397184, 83668255425284801560576, 1171355575953987221848064, 16398978063355821105872896, 229585692886981495482220544, 3214199700417740936751087616, 44998795805848373114515226624, …

Powers of 15: 1, 15, 225, 3375, 50625, 759375, 11390625, 170859375, 2562890625, 38443359375, 576650390625, 8649755859375, 129746337890625, 1946195068359375, 29192926025390625, 437893890380859375, 6568408355712890625, 98526125335693359375, 1477891880035400390625, 22168378200531005859375, 332525673007965087890625, 4987885095119476318359375, 74818276426792144775390625, 1122274146401882171630859375, 16834112196028232574462890625, 252511682940423488616943359375, …

Powers of 16: 1, 16, 256, 4096, 65536, 1048576, 16777216, 268435456, 4294967296, 68719476736, 1099511627776, 17592186044416, 281474976710656, 4503599627370496, 72057594037927936, 1152921504606846976, 18446744073709551616, 295147905179352825856, 4722366482869645213696, 75557863725914323419136, 1208925819614629174706176, 19342813113834066795298816, 309485009821345068724781056, 4951760157141521099596496896, 79228162514264337593543950336, 1267650600228229401496703205376, …

Powers of 17: 1, 17, 289, 4913, 83521, 1419857, 24137569, 410338673, 6975757441, 118587876497, 2015993900449, 34271896307633, 582622237229761, 9904578032905937, 168377826559400929, 2862423051509815793, 48661191875666868481, 827240261886336764177, 14063084452067724991009, 239072435685151324847153, 4064231406647572522401601, 69091933913008732880827217, 1174562876521148458974062689, 19967568900859523802559065713, 339448671314611904643504117121, 5770627412348402378939569991057, …

Powers of 18: 1, 18, 324, 5832, 104976, 1889568, 34012224, 612220032, 11019960576, 198359290368, 3570467226624, 64268410079232, 1156831381426176, 20822964865671168, 374813367582081024, 6746640616477458432, 121439531096594251776, 2185911559738696531968, 39346408075296537575424, 708235345355337676357632, 12748236216396078174437376, 229468251895129407139872768, 4130428534112329328517709824, 74347713614021927913318776832, 1338258845052394702439737982976, 24088659210943104643915283693568, …

Powers of 19: 1, 19, 361, 6859, 130321, 2476099, 47045881, 893871739, 16983563041, 322687697779, 6131066257801, 116490258898219, 2213314919066161, 42052983462257059, 799006685782884121, 15181127029874798299, 288441413567621167681, 5480386857784802185939, 104127350297911241532841, 1978419655660313589123979, 37589973457545958193355601, 714209495693373205673756419, 13569980418174090907801371961, 257829627945307727248226067259, 4898762930960846817716295277921, 93076495688256089536609610280499, …

Powers of 20: 1, 20, 400, 8000, 160000, 3200000, 64000000, 1280000000, 25600000000, 512000000000, 10240000000000, 204800000000000, 4096000000000000, 81920000000000000, 1638400000000000000, 32768000000000000000, 655360000000000000000, 13107200000000000000000, 262144000000000000000000, 5242880000000000000000000, 104857600000000000000000000, 2097152000000000000000000000, 41943040000000000000000000000, 838860800000000000000000000000, 16777216000000000000000000000000, 335544320000000000000000000000000, …

## Powers and related

Perfect powers: 1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 100, 121, 125, 128, 144, 169, 196, 216, 225, 243, 256, 289, 324, 343, 361, 400, 441, 484, 512, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1000, 1024, 1089, 1156, 1225, 1296, 1331, 1369, 1444, 1521, 1600, 1681, 1728, 1764, 1849, 1936, 2025, 2048, 2116, 2187, 2197, 2209, 2304, 2401, 2500, 2601, 2704, 2744, 2809, 2916, 3025, 3125, 3136, 3249, 3364, 3375, 3481, 3600, 3721, 3844, 3969, 4096, 4225, 4356, 4489, 4624, 4761, 4900, 4913, 5041, 5184, 5329, 5476, 5625, 5776, 5832, 5929, 6084, 6241, 6400, 6561, 6724, 6859, 6889, 7056, 7225, 7396, 7569, 7744, 7776, 7921, 8000, 8100, 8192, 8281, 8464, 8649, 8836, 9025, 9216, 9261, 9409, 9604, 9801, 10000, 10201, 10404, 10609, 10648, 10816, 11025, 11236, 11449, 11664, 11881, 12100, 12167, 12321, 12544, 12769, 12996, 13225, 13456, 13689, 13824, 13924, 14161, 14400, 14641, 14884, 15129, 15376, 15625, 15876, 16129, 16384, 16641, 16807, 16900, 17161, 17424, 17576, 17689, 17956, 18225, 18496, 18769, 19044, 19321, 19600, 19683, 19881, …

Powerful numbers: 1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, 108, 121, 125, 128, 144, 169, 196, 200, 216, 225, 243, 256, 288, 289, 324, 343, 361, 392, 400, 432, 441, 484, 500, 512, 529, 576, 625, 648, 675, 676, 729, 784, 800, 841, 864, 900, 961, 968, 972, 1000, 1024, 1089, 1125, 1152, 1156, 1225, 1296, 1323, 1331, 1352, 1369, 1372, 1444, 1521, 1568, 1600, 1681, 1728, 1764, 1800, 1849, 1936, 1944, 2000, 2025, 2048, 2116, 2187, 2197, 2209, 2304, 2312, 2401, 2500, 2592, 2601, 2700, 2704, 2744, 2809, 2888, 2916, 3025, 3087, 3125, 3136, 3200, 3249, 3267, 3364, 3375, 3456, 3481, 3528, 3600, 3721, 3844, 3872, 3888, 3969, 4000, 4096, 4225, 4232, 4356, 4489, 4500, 4563, 4608, 4624, 4761, 4900, 4913, 5000, 5041, 5184, 5292, 5324, 5329, 5400, 5408, 5476, 5488, 5625, 5776, 5832, 5929, 6075, 6084, 6125, 6241, 6272, 6400, 6561, 6724, 6728, 6859, 6889, 6912, 7056, 7200, 7225, 7396, 7569, 7688, 7744, 7776, 7803, 7921, 8000, 8100, 8192, 8281, 8464, 8575, 8649, 8712, 8748, 8788, 8836, 9000, 9025, 9216, 9248, 9261, 9409, 9604, 9747, 9800, 9801, 10000, 10125, 10201, 10368, 10404, 10584, 10609, 10648, 10800, 10816, 10952, 10976, 11025, 11236, 11449, 11552, 11664, 11881, 11907, 11979, 12100, 12167, 12168, 12321, 12348, 12500, 12544, 12769, 12800, 12996, 13068, 13225, 13448, 13456, 13500, 13689, 13824, 13924, 14112, 14161, 14283, 14400, 14641, 14792, 14884, 15125, 15129, 15376, 15488, 15552, 15625, 15876, 16000, 16129, 16200, 16384, 16641, 16807, 16875, 16900, 16928, 17161, 17424, 17496, 17576, 17672, 17689, 17956, 18000, 18225, 18252, 18432, 18496, 18769, 19044, 19208, 19321, 19600, 19652, 19683, 19773, 19881, 20000, …

Achilles numbers: 72, 108, 200, 288, 392, 432, 500, 648, 675, 800, 864, 968, 972, 1125, 1152, 1323, 1352, 1372, 1568, 1800, 1944, 2000, 2312, 2592, 2700, 2888, 3087, 3200, 3267, 3456, 3528, 3872, 3888, 4000, 4232, 4500, 4563, 4608, 5000, 5292, 5324, 5400, 5408, 5488, 6075, 6125, 6272, 6728, 6912, 7200, 7688, 7803, 8575, 8712, 8748, 8788, 9000, 9248, 9747, 9800, 10125, 10368, 10584, 10800, 10952, 10976, 11552, 11907, 11979, 12168, 12348, 12500, 12800, 13068, 13448, 13500, 14112, 14283, 14792, 15125, 15488, 15552, 16000, 16200, 16875, 16928, 17496, 17672, 18000, 18252, 18432, 19208, 19652, 19773, 20000, 20808, 21125, 21168, 21296, 21600, 21632, 22472, 22707, 23328, 24200, 24300, 24500, 24696, 25000, 25088, 25947, 25992, 26136, 26912, 27436, 27648, 27783, 27848, 28125, 28800, 29403, 29768, 30375, 30752, 31104, 31212, 31752, 32000, 33075, 33275, 33800, 34300, 34848, 34992, 35152, 35912, 36000, 36125, 36504, 36963, 36992, 37044, 38088, 38988, 39200, 40328, 40500, 41067, 41472, 41503, 42336, 42592, 42632, 43200, 43808, 43904, 44217, 45000, 45125, 45387, 46208, 47432, 47628, 47916, 48600, 48668, 48672, 49000, 49392, 49923, 49928, 50000, 51200, 52272, 52488, 53792, 54000, 54675, 54925, 55112, 55125, 55296, 56448, 57132, 57800, 57967, 59168, 59643, 60500, 60552, 61731, 61952, 62208, 62424, 63368, 64800, 64827, 65219, 66125, 66248, 67228, 67500, 67712, 68600, 69192, 69984, 70227, 70304, 70688, 72000, 72200, 73008, 73728, 75272, 75843, 76832, 77175, 77976, 78408, 78608, 78732, 79092, 80000, 81000, 81608, 81675, 83232, 83349, 84375, 84500, 84672, 84872, 86400, 86528, 87723, 87808, 88200, 89888, 90828, 91592, 93312, 93987, 95048, 95256, 95832, 96800, 97200, 97556, 98000, 98568, 98784, 99127, …

## By d(*n*)

Highly composite numbers: 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560, 10080, 15120, 20160, 25200, 27720, 45360, 50400, 55440, 83160, 110880, 166320, 221760, 277200, 332640, 498960, 554400, 665280, 720720, 1081080, 1441440, 2162160, 2882880, 3603600, 4324320, 6486480, 7207200, 8648640, 10810800, 14414400, 17297280, 21621600, 32432400, 36756720, 43243200, 61261200, 73513440, 110270160, 122522400, 147026880, 183783600, 245044800, 294053760, 367567200, 551350800, 698377680, 735134400, 1102701600, 1396755360, 2095133040, 2205403200, 2327925600, 2793510720, 3491888400, 4655851200, 5587021440, 6983776800, 10475665200, 13967553600, 20951330400, 27935107200, 41902660800, 48886437600, 64250746560, 73329656400, 80313433200, 97772875200, 128501493120, 146659312800, 160626866400, 240940299600, 293318625600, 321253732800, 481880599200, 642507465600, 963761198400, 1124388064800, 1606268664000, 1686582097200, 1927522396800, 2248776129600, 3212537328000, 3373164194400, 4497552259200, 6746328388800, 8995104518400, 9316358251200, 13492656777600, 18632716502400, 26985313555200, 27949074753600, 32607253879200, 46581791256000, 48910880818800, 55898149507200, 65214507758400, 93163582512000, 97821761637600, 130429015516800, 195643523275200, 260858031033600, 288807105787200, 391287046550400, 577614211574400, 782574093100800, 866421317361600, 1010824870255200, 1444035528936000, 1516237305382800, 1732842634723200, 2021649740510400, 2888071057872000, 3032474610765600, 4043299481020800, 6064949221531200, 8086598962041600, … (all terms > 48 end with 0)

Highly abundant numbers: 1, 2, 3, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 42, 48, 60, 72, 84, 90, 96, 108, 120, 144, 168, 180, 210, 216, 240, 288, 300, 336, 360, 420, 480, 504, 540, 600, 630, 660, 720, 840, 960, 1008, 1080, 1200, 1260, 1440, 1560, 1620, 1680, 1800, 1920, 1980, 2100, 2160, 2340, 2400, 2520, 2880, 3024, 3120, 3240, 3360, 3600, 3780, 3960, 4200, 4320, 4620, 4680, 5040, 5760, 5880, 6120, 6240, 6300, 6720, 7200, 7560, 7920, 8400, 8820, 9240, 10080, 10920, 11340, 11760, 11880, 12240, 12600, 13440, 13860, 15120, 16380, 16800, 17640, 18480, 19800, 20160, 21840, 22680, 23760, 25200, 27720, 30240, 32760, 35280, 36960, 37800, 39600, 40320, 41580, 42840, 43680, 45360, 47520, 47880, 49140, 50400, 52920, 54600, 55440, 60480, 64680, 65520, 70560, 73080, 73920, 75600, 80640, 83160, 85680, 90720, 92400, 95760, 98280, 100800, 105840, 109200, 110880, 120120, 120960, 126000, 128520, 131040, 138600, 147840, 151200, 161280, 163800, 166320, 180180, 181440, 184800, 191520, 194040, 196560, 211680, 214200, 218400, 221760, 239400, 240240, 249480, 257040, 262080, 277200, 294840, 302400, 314160, 327600, 332640, 360360, 383040, 388080, 393120, 415800, 428400, 443520, 458640, 471240, 480480, 491400, 498960, 514080, 524160, 526680, 540540, 554400, 582120, 589680, 604800, 609840, 622440, 637560, 655200, 665280, 718200, 720720, 776160, 786240, 831600, 887040, 914760, 917280, 942480, 982800, 997920, …

Superabundant numbers: 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 10080, 15120, 25200, 27720, 55440, 110880, 166320, 277200, 332640, 554400, 665280, 720720, 1441440, 2162160, 3603600, 4324320, 7207200, 8648640, 10810800, 21621600, 36756720, 61261200, 73513440, 122522400, 147026880, 183783600, 367567200, 698377680, 735134400, 1102701600, 1163962800, 1396755360, 2327925600, 2793510720, 3491888400, 6983776800, 13967553600, 20951330400, 27935107200, 41902660800, 48886437600, 80313433200, 160626866400, 321253732800, 481880599200, 642507465600, 963761198400, 1124388064800, 1927522396800, 2248776129600, 3373164194400, 4497552259200, 4658179125600, 6746328388800, 9316358251200, 13974537376800, 18632716502400, 27949074753600, 32607253879200, 55898149507200, 65214507758400, 97821761637600, 130429015516800, 144403552893600, 195643523275200, 288807105787200, 433210658680800, 577614211574400, 866421317361600, 1010824870255200, 1732842634723200, 2021649740510400, 3032474610765600, 4043299481020800, 6064949221531200, …

Superior highly composite numbers: 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, 1441440, 4324320, 21621600, 367567200, 6983776800, 13967553600, 321253732800, 2248776129600, 65214507758400, 195643523275200, 6064949221531200, 12129898443062400, 448806242393308800, 18401055938125660800, 791245405339403414400, 37188534050951960476800, 185942670254759802384000, 9854961523502269526352000, 581442729886633902054768000, 1162885459773267804109536000, 12791740057505945845204896000, 780296143507862696557498656000, 2340888430523588089672495968000, 156839524845080402008057229856000, 11135606264000708542572063319776000, 812899257272051723607760622343648000, 64219041324492086165013089165148192000, 834847537218397120145170159146926496000, 69292345589126960972049123209194899168000, 6167018757432299526512371965618346025952000, 12334037514864599053024743931236692051904000, 1196401638941866108143400161329959129034688000, 120836565533128476922483416294325872032503488000, 12446166249912233123015791878315564819347859264000, 1331739788740608944162689730979765435670220941248000, 9322178521184262609138828116858358049691546588736000, 1016117458809084624396132264737561027416378578172224000,
114821272845426562556762945915344396098050779333461312000, 1951961638372251563464970080560854733666863248668842304000, 247899128073275948560051200231228551175691632580942972608000, …

Colossally abundant numbers: 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, 1441440, 4324320, 21621600, 367567200, 6983776800, 160626866400, 321253732800, 9316358251200, 288807105787200, 2021649740510400, 6064949221531200, 224403121196654400, 9200527969062830400, 395622702669701707200, 791245405339403414400, 37188534050951960476800, 1970992304700453905270400, 116288545977326780410953600, 581442729886633902054768000, 35468006523084668025340848000, 2376356437046672757697836816000, 168721307030313765796546413936000, 12316655413212904903147888217328000, 135483209545341953934626770390608000, 10703173554082014360835514860858032000, 21406347108164028721671029721716064000, 1776726809977614383898695466902433312000, 5330180429932843151696086400707299936000, 474386058264023040500951689662949694304000, 46015447651610234928592313897306120347488000, 598200819470933054071700080664979564517344000, 60418282766564238461241708147162936016251744000, 6223083124956116561507895939157782409673929632000, 665869894370304472081344865489882717835110470624000, 72579818486363187456866590338397216244027041298016000, 8201519488959040182625924708238885435575055666675808000, 1041592975097798103193492437946338450318032069667827616000, 136448679737811551518347509370970336991662201126485417696000, 18693469124080182558013608783822936167857721554328502224352000, 2598392208247145375563891620951388127332223296051661809184928000, …

Unitary highly abundant numbers: 1, 2, 3, 4, 5, 6, 10, 12, 14, 18, 21, 22, 26, 30, 42, 60, 66, 78, 90, 102, 114, 130, 138, 150, 170, 174, 186, 210, 294, 318, 330, 390, 462, 510, 546, 570, 690, 798, 858, 870, 930, 1050, 1110, 1218, 1230, 1290, 1410, 1470, 1554, 1590, 1722, 1770, 1830, 1974, 2010, 2130, 2190, 2310, 2730, 3390, 3570, 3990, 4290, 4830, 5610, 6006, 6090, 6510, 7410, 7590, 7770, 8610, 9030, 9570, 9870, 11130, 12090, 12210, 12390, 12810, 13530, 14070, 14910, 15330, 16170, 16590, 17430, 18690, 20130, 20370, 21210, 21630, 22470, 22890, 23730, 25410, 26670, 27510, 28770, 29190, 30030, 35490, 36330, 37590, 38010, 39270, 43890, 46410, 51870, 53130, 60690, 61530, 62790, 66990, 71610, 79170, 82110, 84630, 85470, 91770, 94710, 99330, 101010, 103530, 108570, 111930, 115710, 117390, 122430, 128310, 132090, 136290, 140910, 144690, 147630, 149730, 153510, 154770, 161070, 164010, 166530, 168630, 178710, 182490, 189210, 191730, 199290, 205590, 215670, 224070, 233310, 237930, 242970, 247170, 251790, 260610, 261030, 264810, 275730, 281190, 291270, 292110, 293370, 297570, 302610, 308490, 315210, 316470, 321090, 330330, 342930, 344190, 348810, 357630, 362670, 374010, 376530, 385770, 390390, 399630, 406770, 412230, 413490, 418110, 428610, 441210, 445830, 455070, 459690, 472290, 482790, 487410, 494130, 506730, 510510, 570570, 649110, 653730, 667590, 676830, 690690, 746130, 833910, 847770, 861630, 870870, 903210, 930930, …

Bi-unitary highly abundant numbers: 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18, 21, 22, 24, 30, 40, 42, 48, 54, 66, 72, 78, 88, 96, 120, 160, 168, 210, 216, 240, 264, 312, 330, 360, 378, 384, 408, 456, 480, 600, 648, 672, 840, 1056, 1080, 1320, 1512, 1560, 1680, 1848, 1920, 2040, 2184, 2280, 2640, 2688, 2760, 3000, 3192, 3240, 3360, 4200, 4320, 5160, 5280, 6048, 6240, 6720, 7392, 7560, 9120, 9240, 10920, 11880, 13440, 14040, 14280, 15960, 17160, 17280, 18360, 19320, 20520, 21000, 22440, 22680, 24192, 24360, 26040, 26880, 28728, 29568, 29640, 30240, 36120, 36960, 43680, 47520, 53760, 56160, 57120, 60480, 63840, 68040, 73440, 73920, 77280, 82080, 83160, 97440, 98280, 114240, 118560, 120120, 120960, 128520, 143640, 147840, 154440, 157080, 173880, 185640, 189000, 201960, 207480, 212520, 219240, 228480, 231000, 234360, 241920, 249480, 255360, 266760, 267960, 272160, 286440, 294840, 295680, 309120, 309960, 325080, 332640, 389760, 393120, 446040, 461160, 480480, 514080, 574560, 617760, 628320, 665280, 695520, 742560, 748440, 786240, 807840, 829920, 850080, 876960, 884520, 924000, 937440, 997920, …

## *p*-smooth numbers

3-smooth numbers (also called harmonic numbers): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 128, 144, 162, 192, 216, 243, 256, 288, 324, 384, 432, 486, 512, 576, 648, 729, 768, 864, 972, 1024, 1152, 1296, 1458, 1536, 1728, 1944, 2048, 2187, 2304, 2592, 2916, 3072, 3456, 3888, 4096, 4374, 4608, 5184, 5832, 6144, 6561, 6912, 7776, 8192, 8748, 9216, 10368, 11664, 12288, 13122, 13824, 15552, 16384, 17496, 18432, 19683, 20736, 23328, 24576, 26244, 27648, 31104, 32768, 34992, 36864, 39366, 41472, 46656, 49152, 52488, 55296, 59049, 62208, 65536, 69984, 73728, 78732, 82944, 93312, 98304, 104976, 110592, 118098, 124416, 131072, 139968, 147456, 157464, 165888, 177147, 186624, 196608, 209952, 221184, 236196, 248832, 262144, 279936, 294912, 314928, 331776, 354294, 373248, 393216, 419904, 442368, 472392, 497664, 524288, 531441, 559872, 589824, 629856, 663552, 708588, 746496, 786432, 839808, 884736, 944784, 995328, …

5-smooth numbers (also called regular numbers): 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80, 81, 90, 96, 100, 108, 120, 125, 128, 135, 144, 150, 160, 162, 180, 192, 200, 216, 225, 240, 243, 250, 256, 270, 288, 300, 320, 324, 360, 375, 384, 400, 405, 432, 450, 480, 486, 500, 512, 540, 576, 600, 625, 640, 648, 675, 720, 729, 750, 768, 800, 810, 864, 900, 960, 972, 1000, 1024, 1080, 1125, 1152, 1200, 1215, 1250, 1280, 1296, 1350, 1440, 1458, 1500, 1536, 1600, 1620, 1728, 1800, 1875, 1920, 1944, 2000, 2025, 2048, 2160, 2187, 2250, 2304, 2400, 2430, 2500, 2560, 2592, 2700, 2880, 2916, 3000, 3072, 3125, 3200, 3240, 3375, 3456, 3600, 3645, 3750, 3840, 3888, 4000, 4050, 4096, 4320, 4374, 4500, 4608, 4800, 4860, 5000, 5120, 5184, 5400, 5625, 5760, 5832, 6000, 6075, 6144, 6250, 6400, 6480, 6561, 6750, 6912, 7200, 7290, 7500, 7680, 7776, 8000, 8100, 8192, 8640, 8748, 9000, 9216, 9375, 9600, 9720, 10000, 10125, 10240, 10368, 10800, 10935, 11250, 11520, 11664, 12000, 12150, 12288, 12500, 12800, 12960, 13122, 13500, 13824, 14400, 14580, 15000, 15360, 15552, 15625, 16000, 16200, 16384, 16875, 17280, 17496, 18000, 18225, 18432, 18750, 19200, 19440, 19683, 20000, 20250, 20480, 20736, 21600, 21870, 22500, 23040, 23328, 24000, 24300, 24576, 25000, 25600, 25920, 26244, 27000, 27648, 28125, 28800, 29160, 30000, 30375, 30720, 31104, 31250, 32000, 32400, 32768, 32805, 33750, 34560, 34992, 36000, 36450, 36864, 37500, 38400, 38880, 39366, 40000, 40500, 40960, 41472, 43200, 43740, 45000, 46080, 46656, 46875, 48000, 48600, 49152, 50000, 50625, 51200, 51840, 52488, 54000, 54675, 55296, 56250, 57600, 58320, 59049, 60000, 60750, 61440, 62208, 62500, 64000, 64800, 65536, 65610, 67500, 69120, 69984, 72000, 72900, 73728, 75000, 76800, 77760, 78125, 78732, 80000, 81000, 81920, 82944, 84375, 86400, 87480, 90000, 91125, 92160, 93312, 93750, 96000, 97200, 98304, 98415, …

7-smooth numbers (also called humble numbers or highly composite numbers, but this is generally refers to having more divisors than any smaller positive integer): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 49, 50, 54, 56, 60, 63, 64, 70, 72, 75, 80, 81, 84, 90, 96, 98, 100, 105, 108, 112, 120, 125, 126, 128, 135, 140, 144, 147, 150, 160, 162, 168, 175, 180, 189, 192, 196, 200, 210, 216, 224, 225, 240, 243, 245, 250, 252, 256, 270, 280, 288, 294, 300, 315, 320, 324, 336, 343, 350, 360, 375, 378, 384, 392, 400, 405, 420, 432, 441, 448, 450, 480, 486, 490, 500, 504, 512, 525, 540, 560, 567, 576, 588, 600, 625, 630, 640, 648, 672, 675, 686, 700, 720, 729, 735, 750, 756, 768, 784, 800, 810, 840, 864, 875, 882, 896, 900, 945, 960, 972, 980, 1000, 1008, 1024, 1029, 1050, 1080, 1120, 1125, 1134, 1152, 1176, 1200, 1215, 1225, 1250, 1260, 1280, 1296, 1323, 1344, 1350, 1372, 1400, 1440, 1458, 1470, 1500, 1512, 1536, 1568, 1575, 1600, 1620, 1680, 1701, 1715, 1728, 1750, 1764, 1792, 1800, 1875, 1890, 1920, 1944, 1960, 2000, 2016, 2025, 2048, 2058, 2100, 2160, 2187, 2205, 2240, 2250, 2268, 2304, 2352, 2400, 2401, 2430, 2450, 2500, 2520, 2560, 2592, 2625, 2646, 2688, 2700, 2744, 2800, 2835, 2880, 2916, 2940, 3000, 3024, 3072, 3087, 3125, 3136, 3150, 3200, 3240, 3360, 3375, 3402, 3430, 3456, 3500, 3528, 3584, 3600, 3645, 3675, 3750, 3780, 3840, 3888, 3920, 3969, 4000, 4032, 4050, 4096, 4116, 4200, 4320, 4374, 4375, 4410, 4480, 4500, 4536, 4608, 4704, 4725, 4800, 4802, 4860, 4900, 5000, 5040, 5103, 5120, 5145, 5184, 5250, 5292, 5376, 5400, 5488, 5600, 5625, 5670, 5760, 5832, 5880, 6000, 6048, 6075, 6125, 6144, 6174, 6250, 6272, 6300, 6400, 6480, 6561, 6615, 6720, 6750, 6804, 6860, 6912, 7000, 7056, 7168, 7200, 7203, 7290, 7350, 7500, 7560, 7680, 7776, 7840, 7875, 7938, 8000, 8064, 8100, 8192, 8232, 8400, 8505, 8575, 8640, 8748, 8750, 8820, 8960, 9000, 9072, 9216, 9261, 9375, 9408, 9450, 9600, 9604, 9720, 9800, …

11-smooth numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 49, 50, 54, 55, 56, 60, 63, 64, 66, 70, 72, 75, 77, 80, 81, 84, 88, 90, 96, 98, 99, 100, 105, 108, 110, 112, 120, 121, 125, 126, 128, 132, 135, 140, 144, 147, 150, 154, 160, 162, 165, 168, 175, 176, 180, 189, 192, 196, 198, 200, 210, 216, 220, 224, 225, 231, 240, 242, 243, 245, 250, 252, 256, 264, 270, 275, 280, 288, 294, 297, 300, 308, 315, 320, 324, 330, 336, 343, 350, 352, 360, 363, 375, 378, 384, 385, 392, 396, 400, 405, 420, 432, 440, 441, 448, 450, 462, 480, 484, 486, 490, 495, 500, 504, 512, 525, 528, 539, 540, 550, 560, 567, 576, 588, 594, 600, 605, 616, 625, 630, 640, 648, 660, 672, 675, 686, 693, 700, 704, 720, 726, 729, 735, 750, 756, 768, 770, 784, 792, 800, 810, 825, 840, 847, 864, 875, 880, 882, 891, 896, 900, 924, 945, 960, 968, 972, 980, 990, 1000, 1008, 1024, 1029, 1050, 1056, 1078, 1080, 1089, 1100, 1120, 1125, 1134, 1152, 1155, 1176, 1188, 1200, 1210, 1215, 1225, 1232, 1250, 1260, 1280, 1296, 1320, 1323, 1331, 1344, 1350, 1372, 1375, 1386, 1400, 1408, 1440, 1452, 1458, 1470, 1485, 1500, 1512, 1536, 1540, 1568, 1575, 1584, 1600, 1617, 1620, 1650, 1680, 1694, 1701, 1715, 1728, 1750, 1760, 1764, 1782, 1792, 1800, 1815, 1848, 1875, 1890, 1920, 1925, 1936, 1944, 1960, 1980, 2000, …

13-smooth numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 49, 50, 52, 54, 55, 56, 60, 63, 64, 65, 66, 70, 72, 75, 77, 78, 80, 81, 84, 88, 90, 91, 96, 98, 99, 100, 104, 105, 108, 110, 112, 117, 120, 121, 125, 126, 128, 130, 132, 135, 140, 143, 144, 147, 150, 154, 156, 160, 162, 165, 168, 169, 175, 176, 180, 182, 189, 192, 195, 196, 198, 200, 208, 210, 216, 220, 224, 225, 231, 234, 240, 242, 243, 245, 250, 252, 256, 260, 264, 270, 273, 275, 280, 286, 288, 294, 297, 300, 308, 312, 315, 320, 324, 325, 330, 336, 338, 343, 350, 351, 352, 360, 363, 364, 375, 378, 384, 385, 390, 392, 396, 400, 405, 416, 420, 429, 432, 440, 441, 448, 450, 455, 462, 468, 480, 484, 486, 490, 495, 500, 504, 507, 512, 520, 525, 528, 539, 540, 546, 550, 560, 567, 572, 576, 585, 588, 594, 600, 605, 616, 624, 625, 630, 637, 640, 648, 650, 660, 672, 675, 676, 686, 693, 700, 702, 704, 715, 720, 726, 728, 729, 735, 750, 756, 768, 770, 780, 784, 792, 800, 810, 819, 825, 832, 840, 845, 847, 858, 864, 875, 880, 882, 891, 896, 900, 910, 924, 936, 945, 960, 968, 972, 975, 980, 990, 1000, …

17-smooth numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 39, 40, 42, 44, 45, 48, 49, 50, 51, 52, 54, 55, 56, 60, 63, 64, 65, 66, 68, 70, 72, 75, 77, 78, 80, 81, 84, 85, 88, 90, 91, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 117, 119, 120, 121, 125, 126, 128, 130, 132, 135, 136, 140, 143, 144, 147, 150, 153, 154, 156, 160, 162, 165, 168, 169, 170, 175, 176, 180, 182, 187, 189, 192, 195, 196, 198, 200, 204, 208, 210, 216, 220, 221, 224, 225, 231, 234, 238, 240, 242, 243, 245, 250, 252, 255, 256, 260, 264, 270, 272, 273, 275, 280, 286, 288, 289, 294, 297, 300, 306, 308, 312, 315, 320, 324, 325, 330, 336, 338, 340, 343, 350, 351, 352, 357, 360, 363, 364, 374, 375, 378, 384, 385, 390, 392, 396, 400, 405, 408, 416, 420, 425, 429, 432, 440, 441, 442, 448, 450, 455, 459, 462, 468, 476, 480, 484, 486, 490, 495, 500, 504, 507, 510, 512, 520, 525, 528, 539, 540, 544, 546, 550, 560, 561, 567, 572, 576, 578, 585, 588, 594, 595, 600, 605, 612, 616, 624, 625, 630, 637, 640, 648, 650, 660, 663, 672, 675, 676, 680, 686, 693, 700, 702, 704, 714, 715, 720, 726, 728, 729, 735, 748, 750, 756, 765, 768, 770, 780, 784, 792, 800, 810, 816, 819, 825, 832, 833, 840, 845, 847, 850, 858, 864, 867, 875, 880, 882, 884, 891, 896, 900, 910, 918, 924, 935, 936, 945, 952, 960, 968, 972, 975, 980, 990, 1000, …

19-smooth numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 48, 49, 50, 51, 52, 54, 55, 56, 57, 60, 63, 64, 65, 66, 68, 70, 72, 75, 76, 77, 78, 80, 81, 84, 85, 88, 90, 91, 95, 96, 98, 99, 100, 102, 104, 105, 108, 110, 112, 114, 117, 119, 120, 121, 125, 126, 128, 130, 132, 133, 135, 136, 140, 143, 144, 147, 150, 152, 153, 154, 156, 160, 162, 165, 168, 169, 170, 171, 175, 176, 180, 182, 187, 189, 190, 192, 195, 196, 198, 200, 204, 208, 209, 210, 216, 220, 221, 224, 225, 228, 231, 234, 238, 240, 242, 243, 245, 247, 250, 252, 255, 256, 260, 264, 266, 270, 272, 273, 275, 280, 285, 286, 288, 289, 294, 297, 300, 304, 306, 308, 312, 315, 320, 323, 324, 325, 330, 336, 338, 340, 342, 343, 350, 351, 352, 357, 360, 361, 363, 364, 374, 375, 378, 380, 384, 385, 390, 392, 396, 399, 400, 405, 408, 416, 418, 420, 425, 429, 432, 440, 441, 442, 448, 450, 455, 456, 459, 462, 468, 475, 476, 480, 484, 486, 490, 494, 495, 500, 504, 507, 510, 512, 513, 520, 525, 528, 532, 539, 540, 544, 546, 550, 560, 561, 567, 570, 572, 576, 578, 585, 588, 594, 595, 600, 605, 608, 612, 616, 624, 625, 627, 630, 637, 640, 646, 648, 650, 660, 663, 665, 672, 675, 676, 680, 684, 686, 693, 700, 702, 704, 714, 715, 720, 722, 726, 728, 729, 735, 741, 748, 750, 756, 760, 765, 768, 770, 780, 784, 792, 798, 800, 810, 816, 819, 825, 832, 833, 836, 840, 845, 847, 850, 855, 858, 864, 867, 875, 880, 882, 884, 891, 896, 900, 910, 912, 918, 924, 931, 935, 936, 945, 950, 952, 960, 968, 969, 972, 975, 980, 988, 990, 1000, …