300 (number)

301 = 7 × 43 = ${\displaystyle \left\{{7 \atop 3}\right\}}$. 301 is the sum of three consecutive primes (97 + 101 + 103), happy number in base 10,[1] lazy caterer number (sequence A000124 in the OEIS).

302 = 2 × 151. 302 is a nontotient,[2] a happy number,[1] the number of partitions of 40 into prime parts[3]

303 = 3 × 101. 303 is a palindromic semiprime. The number of compositions of 10 which cannot be viewed as stacks is 303.[4]

304 = 2⁴ × 19. 304 is the sum of six consecutive primes (41 + 43 + 47 + 53 + 59 + 61), sum of eight consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), primitive semiperfect number,[5] untouchable number,[6] nontotient.[2] 304 is the smallest number such that no square has a set of digits complementary to the digits of the square of 304: The square of 304 is 92416, while no square exists using the set of the complementary digits 03578.

305 = 5 × 61. 305 is the convolution of the first 7 primes with themselves.[7]

306 = 2 × 3² × 17. 306 is the sum of four consecutive primes (71 + 73 + 79 + 83), pronic number,[8] and an untouchable number.[6]

307 is a prime number, Chen prime,[9] number of one-sided octiamonds[10]

308 = 2² × 7 × 11. 308 is a nontotient,[2] totient sum of the first 31 integers, heptagonal pyramidal number,[11] and the sum of two consecutive primes (151 + 157).

309 = 3 × 103, Blum integer, number of primes <= 2¹¹.[12]

310 = 2 × 5 × 31. 310 is a sphenic number,[13] noncototient,[14] number of Dyck 11-paths with strictly increasing peaks.[15]

312 = 2³ × 3 × 13, idoneal number.

314 = 2 × 157. 314 is a nontotient,[2] smallest composite number in Somos-4 sequence.[16]

315 = 3² × 5 × 7 = ${\displaystyle D_{7,3}\!}$ rencontres number, highly composite odd number, having 12 divisors.[17]

316 = 2² × 79. 316 is a centered triangular number[18] and a centered heptagonal number[19]

317 is a prime number, Eisenstein prime with no imaginary part, Chen prime,[9] and a strictly non-palindromic number.

317 is the exponent (and number of ones) in the fourth base-10 repunit prime.[20]

319 = 11 × 29. 319 is the sum of three consecutive primes (103 + 107 + 109), Smith number,[21] cannot be represented as the sum of fewer than 19 fourth powers, happy number in base 10[1]

320 = 2⁶ × 5 = (2⁵) × (2 × 5). 320 is a Leyland number,[22] and maximum determinant of a 10 by 10 matrix of zeros and ones.

321 = 3 × 107, a Delannoy number[23]

322 = 2 × 7 × 23. 322 is a sphenic,[13] nontotient, untouchable,[6] and a Lucas number.[24]

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.[25] A Lucas and Fibonacci pseudoprime. See 323 (disambiguation)

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,[26] and an untouchable number.[6]

325 = 5² × 13. 325 is a triangular number, hexagonal number,[27] nonagonal number,[28] centered nonagonal number.[29] 325 is the smallest number to be the sum of two squares in 3 different ways: 1² + 18², 6² + 17² and 10² + 15². 325 is also the smallest (and only known) 3-hyperperfect number.

326 = 2 × 163. 326 is a nontotient, noncototient,[14] and an untouchable number.[6] 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 (sequence A000124 in the OEIS).

327 = 3 × 109. 327 is a perfect totient number,[30] number of compositions of 10 whose run-lengths are either weakly increasing or weakly decreasing[31]

328 = 2³ × 41. 328 is a refactorable number,[32] 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 = 7 × 47. 329 is the sum of three consecutive primes (107 + 109 + 113), and a highly cototient number.[33]

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 ${\displaystyle {\tbinom {11}{4}}}$), a pentagonal number,[34] divisible by the number of primes below it, and a sparsely totient number.[35]

331 is a prime number, super-prime, cuban prime,[36] sum of five consecutive primes (59 + 61 + 67 + 71 + 73), centered pentagonal number,[37] centered hexagonal number,[38] and Mertens function returns 0.[39]

332 = 2² × 83, Mertens function returns 0.[39]

333 = 3² × 37, Mertens function returns 0,[39]

334 = 2 × 167, nontotient.[40]

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

336 = 2⁴ × 3 × 7, untouchable number,[6] number of partitions of 41 into prime parts.[3]

337, prime number, emirp, permutable prime with 373 and 733, Chen prime,[9] star number

338 = 2 × 13², nontotient, number of square (0,1)-matrices without zero rows and with exactly 4 entries equal to 1.[41]

339 = 3 × 113, Ulam number[42]

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.[14] 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).

341 = 11 × 31, sum of seven consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61), octagonal number,[43] centered cube number,[44] super-Poulet number. 341 is the smallest Fermat pseudoprime; it is the least composite odd modulus m greater than the base b, that satisfies the Fermat property "b^m−1 − 1 is divisible by m", for bases up to 128 of b = 2, 15, 60, 63, 78, and 108.

342 = 2 × 3² × 19, pronic number,[8] Untouchable number.[6]

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 = 2³ × 43, octahedral number,[45] noncototient,[14] totient sum of the first 33 integers, refactorable number.[32]

345 = 3 × 5 × 23, sphenic number,[13] idoneal number

346 = 2 × 173, Smith number,[21] noncototient.[14]

347 is a prime number, emirp, safe prime,[46] Eisenstein prime with no imaginary part, Chen prime,[9] Friedman prime since 347 = 7³ + 4, and a strictly non-palindromic number.

348 = 2² × 3 × 29, sum of four consecutive primes (79 + 83 + 89 + 97), refactorable number.[32]

349, prime number, sum of three consecutive primes (109 + 113 + 127), 5³⁴⁹ - 4³⁴⁹ is a prime number.[47]

350 = 2 × 5² × 7 = ${\displaystyle \left\{{7 \atop 4}\right\}}$, primitive semiperfect number,[5] divisible by the number of primes below it, nontotient, a truncated icosahedron of frequency 6 has 350 hexagonal faces and 12 pentagonal faces.

351 = 3³ × 13, triangular number, sum of five consecutive primes (61 + 67 + 71 + 73 + 79), member of Padovan sequence[48] and number of compositions of 15 into distinct parts.[49]

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 (sequence A000124 in the OEIS).

354 = 2 × 3 × 59 = 1⁴ + 2⁴ + 3⁴ + 4⁴,[50][51] sphenic number,[13] nontotient, also SMTP code meaning start of mail input. It is also sum of absolute value of the coefficients of Conway's polynomial.

355 = 5 × 71, Smith number,[21] Mertens function returns 0,[39] divisible by the number of primes below it.

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.

356 = 2² × 89, Mertens function returns 0.[39]

357 = 3 × 7 × 17, sphenic number.[13]

358 = 2 × 179, sum of six consecutive primes (47 + 53 + 59 + 61 + 67 + 71), Mertens function returns 0,[39] number of ways to partition {1,2,3,4,5} and then partition each cell (block) into subcells.[52]

361 = 19², centered triangular number,[18] centered octagonal number, centered decagonal number,[53] member of the Mian–Chowla sequence;[54] also the number of positions on a standard 19 x 19 Go board.

362 = 2 × 181 = σ₂(19): sum of squares of divisors of 19,[55] Mertens function returns 0,[39] nontotient, noncototient.[14]

364 = 2² × 7 × 13, tetrahedral number,[56] sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), Mertens function returns 0,[39] 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.[57]

366 = 2 × 3 × 61, sphenic number,[13] Mertens function returns 0,[39] noncototient,[14] number of complete partitions of 20,[58] 26-gonal and 123-gonal.

367 is a prime number, Perrin number,[59] happy number, prime index prime and a strictly non-palindromic number.

368 = 2⁴ × 23. It is also a Leyland number.[22]

370 = 2 × 5 × 37, sphenic number,[13] 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 = 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 (sequence A055233 in the OEIS), the next such composite number is 2935561623745, Armstrong number since 3³ + 7³ + 1³ = 371.

372 = 2² × 3 × 31, sum of eight consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61), noncototient,[14] untouchable number,[6] refactorable number.[32]

373, prime number, balanced prime,[60] two-sided prime, sum of five consecutive primes (67 + 71 + 73 + 79 + 83), permutable prime with 337 and 733, palindromic prime in 3 consecutive bases: 565₈ = 454₉ = 373₁₀ and also in base 4: 11311₄.

374 = 2 × 11 × 17, sphenic number,[13] nontotient, 374⁴ + 1 is prime.[61]

375 = 3 × 5³, number of regions in regular 11-gon with all diagonals drawn.[62]

376 = 2³ × 47, pentagonal number,[34] 1-automorphic number,[63] nontotient, refactorable number.[32] There is a math puzzle in which when 376 is squared, 376 is also the last three digits, as 376 * 376 = 141376 [64]

377 = 13 × 29, Fibonacci number, a centered octahedral number,[65] a Lucas and Fibonacci pseudoprime, the sum of the squares of the first six primes.

378 = 2 × 3³ × 7, triangular number, cake number, hexagonal number,[27] Smith number.[21]

379 is a prime number, Chen prime,[9] lazy caterer number (sequence A000124 in the OEIS) and a happy number in base 10. It is the sum of the 15 consecutive primes (3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53). 379! - 1 is prime.

380 = 2² × 5 × 19, pronic number,[8] 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 OEIS: A306302 and OEIS: A331452.

381 = 3 × 127, palindromic in base 2 and base 8.

It 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 = 2 × 191, sum of ten consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), Smith number.[21]

383, prime number, safe prime,[46] Woodall prime,[66] 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.[67] 4³⁸³ - 3³⁸³ is prime.

385 = 5 × 7 × 11, sphenic number,[13] square pyramidal number,[68] the number of integer partitions of 18.

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

386 = 2 × 193, nontotient, noncototient,[14] centered heptagonal number,[19] number of surface points on a cube with edge-length 9.[69]

387 = 3² × 43, number of graphical partitions of 22.[70]

388 = 2² × 97 = solution to postage stamp problem with 6 stamps and 6 denominations,[71] number of uniform rooted trees with 10 nodes.[72]

389, prime number, emirp, Eisenstein prime with no imaginary part, Chen prime,[9] highly cototient number,[33] strictly non-palindromic number. Smallest conductor of a rank 2 Elliptic curve.

390 = 2 × 3 × 5 × 13, sum of four consecutive primes (89 + 97 + 101 + 103), nontotient,

${\displaystyle \sum _{n=0}^{10}{390}^{n}}$ is prime[73]

391 = 17 × 23, Smith number,[21] centered pentagonal number.[37]

392 = 2³ × 7², Achilles number.

393 = 3 × 131, Blum integer, Mertens function returns 0.[39]

394 = 2 × 197 = S₅ a Schröder number,[74] nontotient, noncototient.[14]

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.[75]

396 = 2² × 3² × 11, sum of twin primes (197 + 199), totient sum of the first 36 integers, refactorable number,[32] Harshad number, digit-reassembly number.

397, prime number, cuban prime,[36] centered hexagonal number.[38]

398 = 2 × 199, nontotient.

${\displaystyle \sum _{n=0}^{10}{398}^{n}}$ is prime[73]

399 = 3 × 7 × 19, sphenic number,[13] smallest Lucas–Carmichael number, Leyland number of the second kind. 399! + 1 is prime.