# 300 (number)

300 (three hundred) is the natural number following 299 and preceding 301.

## In Mathematics

300 is a composite number and the 24th triangular number.

## Integers from 301 to 399
### 310s
#### 310
#### 315

315 = 3$^2$ × 5 × 7 = $D_{7,3}\!$, rencontres number, highly composite odd number, having 12 divisors.
It is a Harshad number, as it is divisible by the sum of its digits.
It is a Zuckerman number, as it is divisible by the product of its digits.

#### 316

316 = 2$^2$ × 79, a centered triangular number and a centered heptagonal number.

#### 317

317 is a prime number, Eisenstein prime with no imaginary part, Chen prime, one of the rare primes to be both right and left-truncatable, and a strictly non-palindromic number.
317 is the exponent (and number of ones) in the fourth base-10 repunit prime.

#### 319

319 = 11 × 29. 319 is the sum of three consecutive primes (103 + 107 + 109), Smith number, cannot be represented as the sum of fewer than 19 fourth powers, happy number in base 10

### 320s
#### 320

320 = 2$^6$ × 5 = (2$^5$) × (2 × 5). 320 is a Leyland number, and maximum determinant of a 10 by 10 matrix of zeros and ones.

#### 321

321 = 3 × 107, a Delannoy number

#### 322

322 = 2 × 7 × 23. 322 is a sphenic, nontotient, untouchable, and a Lucas number. It is also the first unprimeable number to end in 2.

#### 323

323 = 17 × 19. 323 is the sum of nine consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), the sum of the 13 consecutive primes (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47), Motzkin number. A Lucas and Fibonacci pseudoprime. See 323 (disambiguation)

#### 324

324 = 2$^2$ × 3$^4$ = 18$^2$. 324 is the sum of four consecutive primes (73 + 79 + 83 + 89), totient sum of the first 32 integers, a square number, and an untouchable number.

#### 326

326 = 2 × 163. 326 is a nontotient, noncototient, and an untouchable number. 326 is the sum of the 14 consecutive primes (3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47), lazy caterer number

#### 327

327 = 3 × 109. 327 is a perfect totient number, number of compositions of 10 whose run-lengths are either weakly increasing or weakly decreasing

#### 328

328 = 2$^3$ × 41. 328 is a refactorable number, and it is the sum of the first fifteen primes (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47).

#### 329

329 = 7 × 47. 329 is the sum of three consecutive primes (107 + 109 + 113), and a highly cototient number.

### 330s
#### 330

330 = 2 × 3 × 5 × 11. 330 is sum of six consecutive primes (43 + 47 + 53 + 59 + 61 + 67), pentatope number (and hence a binomial coefficient ${\tbinom {11}{4}}$), a pentagonal number, divisible by the number of primes below it, and a sparsely totient number.

#### 331

331 is a prime number, super-prime, cuban prime, a lucky prime, sum of five consecutive primes (59 + 61 + 67 + 71 + 73), centered pentagonal number, centered hexagonal number, and Mertens function returns 0.

#### 332

332 = 2$^2$ × 83, Mertens function returns 0.

#### 333

333 = 3$^2$ × 37, Mertens function returns 0; repdigit; 2$^{333}$ is the smallest power of two greater than a googol.

#### 334

334 = 2 × 167, nontotient.

#### 335

335 = 5 × 67. 335 is divisible by the number of primes below it, number of Lyndon words of length 12.

#### 336

336 = 2$^4$ × 3 × 7, untouchable number, number of partitions of 41 into prime parts, largely composite number.

#### 337

337, prime number, emirp, permutable prime with 373 and 733, Chen prime, star number

#### 338

338 = 2 × 13$^2$, nontotient, number of square (0,1)-matrices without zero rows and with exactly 4 entries equal to 1.

#### 339

339 = 3 × 113, Ulam number

### 340s
#### 340

340 = 2$^2$ × 5 × 17, sum of eight consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), sum of ten consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), sum of the first four powers of 4 (4$^1$ + 4$^2$ + 4$^3$ + 4$^4$), divisible by the number of primes below it, nontotient, noncototient. Number of regions formed by drawing the line segments connecting any two of the 12 perimeter points of a 3 times 3 grid of squares (sequence A331452 in the OEIS) and (sequence A255011 in the OEIS).

#### 342

342 = 2 × 3$^2$ × 19, pronic number, Untouchable number.

#### 343

343 = 7$^3$, the first nice Friedman number that is composite since 343 = (3 + 4)$^3$. It is the only known example of x$^2$+x+1 = y$^3$, in this case, x=18, y=7. It is z$^3$ in a triplet (x,y,z) such that x$^5$ + y$^2$ = z$^3$.

#### 344

344 = 2$^3$ × 43, octahedral number, noncototient, totient sum of the first 33 integers, refactorable number.

#### 345

345 = 3 × 5 × 23, sphenic number, idoneal number

#### 346

346 = 2 × 173, Smith number, noncototient.

#### 347

347 is a prime number, emirp, safe prime, Eisenstein prime with no imaginary part, Chen prime, Friedman prime since 347 = 7$^3$ + 4, twin prime with 349, and a strictly non-palindromic number.

#### 348

348 = 2$^2$ × 3 × 29, sum of four consecutive primes (79 + 83 + 89 + 97), refactorable number.

#### 349

349, prime number, twin prime, lucky prime, sum of three consecutive primes (109 + 113 + 127), 5$^{349}$ - 4$^{349}$ is a prime number.

### 350s
#### 350

350 = 2 × 5$^2$ × 7 = $\left\{{7 \atop 4}\right\}$, primitive semiperfect number, divisible by the number of primes below it, nontotient, a truncated icosahedron of frequency 6 has 350 hexagonal faces and 12 pentagonal faces.

#### 351

351 = 3$^3$ × 13, 26th triangular number, sum of five consecutive primes (61 + 67 + 71 + 73 + 79), member of Padovan sequence and number of compositions of 15 into distinct parts.

#### 352

352 = 2$^5$ × 11, the number of n-Queens Problem solutions for n = 9. It is the sum of two consecutive primes (173 + 179), lazy caterer number

#### 354

354 = 2 × 3 × 59 = 1$^4$ + 2$^4$ + 3$^4$ + 4$^4$, sphenic number, nontotient, also SMTP code meaning start of mail input. It is also sum of absolute value of the coefficients of Conway's polynomial.

#### 355

355 = 5 × 71, Smith number, Mertens function returns 0, divisible by the number of primes below it. The cototient of 355 is 75, where 75 is the product of its digits (3 x 5 x 5 = 75).
The numerator of the best simplified rational approximation of pi having a denominator of four digits or fewer. This fraction (355/113) is known as Milü and provides an extremely accurate approximation for pi, being accurate to seven digits.

#### 356

356 = 2$^2$ × 89, Mertens function returns 0.

#### 357

357 = 3 × 7 × 17, sphenic number.

#### 358

358 = 2 × 179, sum of six consecutive primes (47 + 53 + 59 + 61 + 67 + 71), Mertens function returns 0, number of ways to partition {1,2,3,4,5} and then partition each cell (block) into subcells.

#### 359
### 360s
#### 361

361 = 19$^2$. 361 is a centered triangular number, centered octagonal number, centered decagonal number, member of the Mian–Chowla sequence; also the number of positions on a standard 19 x 19 Go board.

#### 362

362 = 2 × 181 = σ$_2$(19): sum of squares of divisors of 19, Mertens function returns 0, nontotient, noncototient.

#### 364

364 = 2$^2$ × 7 × 13, tetrahedral number, sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), Mertens function returns 0, nontotient. It is a repdigit in base 3 (111111), base 9 (444), base 25 (EE), base 27 (DD), base 51 (77) and base 90 (44), the sum of six consecutive powers of 3 (1 + 3 + 9 + 27 + 81 + 243), and because it is the twelfth non-zero tetrahedral number.

#### 366

366 = 2 × 3 × 61, sphenic number, Mertens function returns 0, noncototient, number of complete partitions of 20, 26-gonal and 123-gonal. Also the number of days in a leap year.

#### 367

367 is a prime number, a lucky prime, Perrin number, happy number, prime index prime and a strictly non-palindromic number.

#### 368

368 = 2$^4$ × 23. It is also a Leyland number.

#### 369
### 370s
#### 370

370 = 2 × 5 × 37, sphenic number, sum of four consecutive primes (83 + 89 + 97 + 101), nontotient, with 369 part of a Ruth–Aaron pair with only distinct prime factors counted, Base 10 Armstrong number since 3$^3$ + 7$^3$ + 0$^3$ = 370.

#### 371

371 = 7 × 53, sum of three consecutive primes (113 + 127 + 131), sum of seven consecutive primes (41 + 43 + 47 + 53 + 59 + 61 + 67), sum of the primes from its least to its greatest prime factor, the next such composite number is 2935561623745, Armstrong number since 3$^3$ + 7$^3$ + 1$^3$ = 371.

#### 372

372 = 2$^2$ × 3 × 31, sum of eight consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61), noncototient, untouchable number, --> refactorable number.

#### 373

373, prime number, balanced prime, one of the rare primes to be both right and left-truncatable (two-sided prime), sum of five consecutive primes (67 + 71 + 73 + 79 + 83), sexy prime with 367 and 379, permutable prime with 337 and 733, palindromic prime in 3 consecutive bases: 565$_8$ = 454$_9$ = 373$_{10}$ and also in base 4: 11311$_4$.

#### 374

374 = 2 × 11 × 17, sphenic number, nontotient, 374$^4$ + 1 is prime.

#### 375

375 = 3 × 5$^3$, number of regions in regular 11-gon with all diagonals drawn.

#### 376

376 = 2$^3$ × 47, pentagonal number, 1-automorphic number, nontotient, refactorable number. There is a math puzzle in which when 376 is squared, 376 is also the last three digits, as 376 * 376 = 141376 It is one of the two three-digit numbers where when squared, the last three digits remain the same.

#### 377

377 = 13 × 29, Fibonacci number, a centered octahedral number, a Lucas and Fibonacci pseudoprime, the sum of the squares of the first six primes.

#### 378

378 = 2 × 3$^3$ × 7, 27th triangular number, cake number, hexagonal number, Smith number.

#### 379

379 is a prime number, Chen prime, lazy caterer number and a happy number in base 10. It is the sum of the first 15 odd primes (3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53). 379! - 1 is prime.

### 380s
#### 380

380 = 2$^2$ × 5 × 19, pronic number, number of regions into which a figure made up of a row of 6 adjacent congruent rectangles is divided upon drawing diagonals of all possible rectangles.

#### 381

381 = 3 × 127, palindromic in base 2 and base 8.
381 is the sum of the first 16 prime numbers (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53).

#### 382

382 = 2 × 191, sum of ten consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), Smith number.

#### 383

383, prime number, safe prime, Woodall prime, Thabit number, Eisenstein prime with no imaginary part, palindromic prime. It is also the first number where the sum of a prime and the reversal of the prime is also a prime. 4$^{383}$ - 3$^{383}$ is prime.

#### 385

385 = 5 × 7 × 11, sphenic number, square pyramidal number, the number of integer partitions of 18.
385 = 10$^2$ + 9$^2$ + 8$^2$ + 7$^2$ + 6$^2$ + 5$^2$ + 4$^2$ + 3$^2$ + 2$^2$ + 1$^2$

#### 386

386 = 2 × 193, nontotient, noncototient, centered heptagonal number, number of surface points on a cube with edge-length 9.

#### 387

387 = 3$^2$ × 43, number of graphical partitions of 22.

#### 388

388 = 2$^2$ × 97 = solution to postage stamp problem with 6 stamps and 6 denominations, number of uniform rooted trees with 10 nodes.

#### 389

389, prime number, emirp, Eisenstein prime with no imaginary part, Chen prime, highly cototient number, strictly non-palindromic number. Smallest conductor of a rank 2 Elliptic curve.

### 390s
#### 390

390 = 2 × 3 × 5 × 13, sum of four consecutive primes (89 + 97 + 101 + 103), nontotient,
    $\sum _{n=0}^{10}{390}^{n}$ is prime

#### 391

391 = 17 × 23, Smith number, centered pentagonal number.

#### 392

392 = 2$^3$ × 7$^2$, Achilles number.

#### 393

393 = 3 × 131, Blum integer, Mertens function returns 0.

#### 394

394 = 2 × 197 = S$_5$ a Schröder number, nontotient, noncototient.

#### 395

395 = 5 × 79, sum of three consecutive primes (127 + 131 + 137), sum of five consecutive primes (71 + 73 + 79 + 83 + 89), number of (unordered, unlabeled) rooted trimmed trees with 11 nodes.

#### 396

396 = 2$^2$ × 3$^2$ × 11, sum of twin primes (197 + 199), totient sum of the first 36 integers, refactorable number, Harshad number, digit-reassembly number.

#### 397

397, prime number, cuban prime, centered hexagonal number.

#### 398

398 = 2 × 199, nontotient.
    $\sum _{n=0}^{10}{398}^{n}$ is prime

#### 399

399 = 3 × 7 × 19, sphenic number, smallest Lucas–Carmichael number, and a Leyland number of the second kind ($4^{5}-5^{4}$). 399! + 1 is prime.