# Harshadgetal

Een harshadgetal of nivengetal is, in een gegeven talstelsel, een geheel getal dat deelbaar is door de som van zijn cijfers. Harshadgetallen in talstelsel met grondtal $n$ worden ook wel aangeduid als $n$-harshad- of $n$-nivengetallen.
De naam nivengetal komt van I.M. Niven, die deze getallen beschreef in een bijdrage op een conferentie over getaltheorie in 1997. Het woord harshad is afgeleid van Sanskriet harṣa, dat 'vreugde' betekent.
Alle gehele getallen van 1 tot en met $n$ en alle n-vouden daarvan zijn $n$-harshadgetallen.
Onderstaande tabel bevat de harshadgetallen tot 100, in talstelsels tot 19.
| grondtal → getal ↓ | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 2 | 10 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| 3 | | 10 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| 4 | 100 | 11 | 10 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| 5 | | | | 10 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| 6 | 110 | 20 | 12 | 11 | 10 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 |
| 7 | | | | | | 10 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 |
| 8 | 1000 | 22 | 20 | 13 | | 11 | 10 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 |
| 9 | | 100 | 21 | | | 12 | | 10 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 |
| 10 | 1010 | 101 | | 20 | 14 | | | 11 | 10 | A | A | A | A | A | A | A | A | A |
| 11 | | | | | | | | | | 10 | B | B | B | B | B | B | B | B |
| 12 | 1100 | 110 | 30 | 22 | 20 | 15 | | 13 | 12 | 11 | 10 | C | C | C | C | C | C | C |
| 13 | | | | | | | | | | | | 10 | D | D | D | D | D | D |
| 14 | | | | | | 20 | 16 | | | | | 11 | 10 | E | E | E | E | E |
| 15 | | 120 | | 30 | 23 | 21 | | | | 14 | | 12 | | 10 | F | F | F | F |
| 16 | 10000 | 121 | 100 | 31 | | 22 | 20 | 17 | | | | 13 | | 11 | 10 | G | G | G |
| 17 | | | | | | | | | | | | | | | | 10 | H | H |
| 18 | 10010 | 200 | 102 | 33 | 30 | 24 | | 20 | 18 | | | 15 | | | 12 | 11 | 10 | I |
| 19 | | | | | | | | | | | | | | | | | | 10 |
| 20 | 10100 | 202 | 110 | 40 | 32 | | | 22 | 20 | 19 | | | | | 14 | 13 | | 11 |
| 21 | 10101 | 210 | 111 | | | 30 | 25 | | 21 | | | | | 16 | | | | 12 |
| 22 | | | | | | | | | | 20 | 1A | | | | | | | |
| 24 | 11000 | 220 | 120 | 44 | 40 | 33 | 30 | 26 | 24 | 22 | 20 | 1B | | | | 17 | | 15 |
| 25 | | 221 | | 100 | 41 | | | | | 23 | | | | | | | | |
| 26 | | | | 101 | | | | | | | | 20 | 1C | | | | | |
| 27 | | 1000 | | 102 | | 36 | | 30 | 27 | | | 21 | | | | | | 18 |
| 28 | | 1001 | 130 | 103 | | 40 | 34 | 31 | | | | 22 | 20 | 1D | | | | |
| 30 | | 1010 | 132 | 110 | 50 | 42 | | 33 | 30 | 28 | | 24 | | 20 | 1E | | | |
| 32 | 100000 | 1012 | 200 | 112 | | 44 | 40 | 35 | | | | 26 | | 22 | 20 | 1F | | |
| 33 | | 1020 | 201 | | | | | | | 30 | 29 | | | | 21 | | | |
| 34 | 100010 | | | | | | | | | | | | | | | 20 | 1G | |
| 35 | | 1022 | 203 | | | 50 | 43 | | | 32 | | | | 25 | 23 | | | |
| 36 | 100100 | 1100 | 210 | 121 | 100 | 51 | | 40 | 36 | 33 | 30 | 2A | | | 24 | 22 | 20 | 1H |
| 38 | | | | | | | | | | | | | | | | | | 20 |
| 39 | | 1110 | | | | | | | | | | 30 | 2B | | | | | 21 |
| 40 | 101000 | 1111 | 220 | 130 | 104 | 55 | 50 | 44 | 40 | 37 | | 31 | | | 28 | 26 | | 22 |
| 42 | 101010 | | 222 | 132 | 110 | 60 | 52 | | 42 | | | 33 | 30 | 2C | | | | 24 |
| 44 | | | | | 112 | | | | | 40 | 38 | | | | | | | |
| 45 | | 1200 | | 140 | 113 | 63 | | 50 | 45 | 41 | | 36 | | 30 | 2D | | | 27 |
| 48 | 110000 | 1210 | 300 | 143 | 120 | 66 | 60 | 53 | 48 | 44 | 40 | 39 | | 33 | 30 | 2E | | 2A |
| 49 | | | | | | 100 | 61 | | | | | | | 34 | | | | |
| 50 | | | 302 | 200 | 122 | 101 | | 55 | 50 | 46 | | | | | 32 | | | |
| 51 | | | | 201 | | 102 | | | | | | | | | | 30 | 2F | |
| 52 | | | 310 | 202 | | 103 | | | | | | 40 | 3A | | | 31 | | |
| 54 | | 2000 | 312 | 204 | | 105 | | 60 | 54 | | | 42 | | | 36 | 33 | 30 | 2G |
| 55 | 110111 | | | | 131 | | | | | 50 | 47 | | | | | | | |
| 56 | | 2002 | | 211 | | 110 | 70 | 62 | | | | 44 | 40 | 3B | | 35 | | |
| 57 | | 2010 | | | | 111 | | | | | | | | | | | | 30 |
| 60 | 111100 | 2020 | 330 | 220 | 140 | 114 | | 66 | 60 | 55 | 50 | 48 | | 40 | 3C | 39 | | 33 |
| 63 | | 2100 | 333 | 223 | | 120 | | 70 | 63 | | | | | 43 | | | | 36 |
| 64 | 1000000 | 2101 | 1000 | 224 | | 121 | 100 | 71 | | | | 4C | | 44 | 40 | 3D | | |
| 65 | | 2102 | | 230 | | 122 | | | | | | 50 | 49 | | 41 | | | |
| 66 | 1000010 | | 1002 | 231 | 150 | 123 | 102 | | | 60 | 56 | 51 | | | 42 | | | |
| 68 | 1000100 | | 1010 | | | | | | | | | | | | | 40 | 3E | |
| 69 | 1000101 | | 1011 | | | | | | | | | | | | | | | |
| 70 | | | | | 154 | | 106 | 77 | 70 | 64 | | 55 | 50 | 4A | 46 | | | |
| 72 | 1001000 | 2200 | 1020 | 242 | 200 | 132 | 110 | 80 | 72 | 66 | 60 | 57 | | | 48 | 44 | 40 | 3F |
| 75 | | 2210 | | 300 | 203 | | 113 | | | 69 | | 5A | | 50 | 4B | | | |
| 76 | | | 1030 | 301 | | | | | | | | | | | | | | 40 |
| 77 | | 2212 | | | 205 | | 115 | | | 70 | 65 | | | 52 | | | | |
| 78 | | 2220 | 1032 | 303 | 210 | 141 | | | | | | 60 | 58 | | | | | 42 |
| 80 | 1010000 | 2222 | 1100 | 310 | 212 | 143 | | 88 | 80 | 73 | | 62 | | 55 | 50 | 4C | | 44 |
| 81 | 1010001 | 10000 | 1101 | | | 144 | | 100 | 81 | | | 63 | | | | | | 45 |
| 82 | | 10001 | | | | | | 101 | | | | | | | | | | |
| 84 | 1010100 | 10010 | 1110 | | 220 | 150 | 124 | 103 | 84 | 77 | 70 | 66 | 60 | 59 | | | | 48 |
| 85 | | | | 320 | 221 | | | 104 | | | | | | | | 50 | 4D | |
| 87 | | 10020 | | | | | | | | | | | | | | | | |
| 88 | | 10021 | 1120 | 323 | 224 | | 130 | 107 | | 80 | 74 | | | | | 53 | | |
| 90 | | 10100 | 1122 | 330 | 230 | | 132 | 110 | 90 | 82 | | 6C | | 60 | 5A | 55 | 50 | 4E |
| 91 | | | 1123 | 331 | | 160 | 133 | | | | | 70 | 67 | 61 | | | | |
| 92 | 1011100 | 10102 | | | | | | 112 | | | | | | | | | | |
| 93 | | 10110 | | | | | | | | | | | | | | | | |
| 95 | | 10112 | | | | | | | | | | | | | | | | 50 |
| 96 | 1100000 | 10120 | 1200 | 341 | 240 | 165 | | 116 | | 88 | 80 | 75 | | 66 | 60 | 5B | | 51 |
| 98 | | | | | | 200 | 142 | | | | | 77 | 70 | 68 | | | | |
| 99 | | 10200 | | 344 | 243 | 201 | | 120 | | 90 | 83 | | | | 63 | | | 54 |