300 (number)

In mathematics

300 is a composite number and the 24th triangular number. It is also a second hexagonal number.

Integers from 301 to 399

300s

301

Main article: 301 (number)

302

Main article: 302 (number)

303

Main article: 303 (number)

304

Main article: 304 (number)

305

Main article: 305 (number)

306

Main article: 306 (number)

307

Main article: 307 (number)

308

Main article: 308 (number)

309

Main article: 309 (number)

310s

310

Main article: 310 (number)

311

Main article: 311 (number)

312

Main article: 312 (number)

313

Main article: 313 (number)

314

Main article: 314 (number)

315

Main article: 315 (number)

316

Main article: 316 (number)

316 = 22 × 79, a centered triangular number and a centered heptagonal number.

317

317 is the smallest natural number that does not have its own Wikipedia article (only a redirect and section), a fact that has itself been noted as making the number notable, creating a situation similar to the interesting number paradox.

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.

318

Main article: 318 (number)

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 = 26 × 5 = (25) × (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

Main article: 323 (number)

324

324 = 22 × 34 = 182. 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.

325

Main article: 325 (number)

326

326 = 2 × 163. 326 is a nontotient, noncototient, and an untouchable 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 = 23 × 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 = 22 × 83, Mertens function returns 0.

333

333 = 32 × 37, Mertens function returns 0; repdigit; 2333 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 = 24 × 3 × 7, untouchable number, largely composite number.

337

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

338

338 = 2 × 132, 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 = 22 × 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 (41 + 42 + 43 + 44), 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 and .

341

Main article: 341 (number)

342

342 = 2 × 32 × 19, pronic number, Untouchable number.

343

343 = 73, the first nice Friedman number that is composite since 343 = (3 + 4)3. It is the only known example of x2+x+1 = y3, in this case, x=18, y=7. It is z3 in a triplet (x,y,z) such that x5 + y2 = z3.

344

344 = 23 × 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.

348

348 = 22 × 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), 5349 - 4349 is a prime number.

350s

350

350 = 2 × 52 × 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 = 33 × 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.

• The international calling code for Portugal

352

352 = 25 × 11, the number of n-Queens Problem solutions for n = 9. It is the sum of two consecutive primes (173 + 179), lazy caterer number

• The international calling code for Luxembourg

353

Main article: 353 (number)

• The international calling code for Republic of Ireland

354

354 = 2 × 3 × 59 = 14 + 24 + 34 + 44,{{cite OEIS| A031971|2=a(n) = Sum_{k=1..n} k^n}} 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.

• The international calling code for Iceland

355

355 = 5 × 71, Smith number, 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 = 22 × 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,

• The international calling code for Finland

359

Main article: 359 (number)

360s

360

Main article: 360 (number)

361

361 = 192. 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 = σ2(19): sum of squares of divisors of 19, Mertens function returns 0, nontotient, noncototient.

363

Main article: 363 (number)

364

364 = 22 × 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.

365

Main article: 365 (number)

366

366 = 2 × 3 × 61, sphenic number, 26-gonal and 123-gonal. Also the number of days in a leap year.

367

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

368

368 = 24 × 23. It is also a Leyland number.

369

Main article: 369 (number)

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 33 + 73 + 03 = 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 33 + 73 + 13 = 371.

372

372 = 22 × 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: 5658 = 4549 = 37310 and also in base 4: 113114.

374

374 = 2 × 11 × 17, sphenic number,

375

375 = 3 × 53, number of regions in regular 11-gon with all diagonals drawn.

376

376 = 23 × 47, pentagonal number, nontotient, refactorable number.

377

Main article: 377 (number)

378

378 = 2 × 33 × 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 = 22 × 5 × 19, pronic number,

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. 4383 - 3383 is prime.

384

Main article: 384 (number)

385

385 = 5 × 7 × 11, sphenic number, the number of integer partitions of 18.

385 = 102 + 92 + 82 + 72 + 62 + 52 + 42 + 32 + 22 + 12

386

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

387

387 = 32 × 43, number of graphical partitions of 22.

388

388 = 22 × 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 = 23 × 72, Achilles number.

393

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

394

394 = 2 × 197 = S5 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 = 22 × 32 × 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, 399! + 1 is prime.

References

References

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