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300 (number)

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

← 299 300 301 →
Cardinalthree hundred
Ordinal300th
(three hundredth)
Factorization22 × 3 × 52
Greek numeralΤ´
Roman numeralCCC
Binary1001011002
Ternary1020103
Senary12206
Octal4548
Duodecimal21012
Hexadecimal12C16
Hebrewש (Shin)

Mathematical properties edit

The number 300 is a triangular number and the sum of a pair of twin primes (149 + 151), as well as the sum of ten consecutive primes (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47). It is palindromic in 3 consecutive bases: 30010 = 6067 = 4548 = 3639, and also in base 13. Factorization is 22 × 3 × 52. 30064 + 1 is prime

Integers from 301 to 399 edit

300s edit

301 edit

Main article: 301 (number)

302 edit

Main article: 302 (number)

303 edit

303 = 3 × 101. 303 is a palindromic semiprime. The number of compositions of 10 which cannot be viewed as stacks is 303.[1]

304 edit

Main article: 304 (number)

305 edit

305 = 5 × 61. 305 is the convolution of the first 7 primes with themselves.[2]

306 edit

306 = 2 × 32 × 17. 306 is the sum of four consecutive primes (71 + 73 + 79 + 83), pronic number,[3] and an untouchable number.[4]

307 edit

Main article: 307 (number)

308 edit

308 = 22 × 7 × 11. 308 is a nontotient,[5] totient sum of the first 31 integers, heptagonal pyramidal number,[6] and the sum of two consecutive primes (151 + 157).

309 edit

309 = 3 × 103, Blum integer, number of primes <= 211.[7]

310s edit

310 edit

Main article: 310 (number)

311 edit

Main article: 311 (number)

312 edit

Main article: 312 (number)

312 = 23 × 3 × 13, idoneal number.

313 edit

Main article: 313 (number)

314 edit

314 = 2 × 157. 314 is a nontotient,[8] smallest composite number in Somos-4 sequence.[9]

315 edit

315 = 32 × 5 × 7 =   rencontres number, highly composite odd number, having 12 divisors.[10]

316 edit

316 = 22 × 79. 316 is a centered triangular number[11] and a centered heptagonal number[12]

317 edit

317 is a prime number, Eisenstein prime with no imaginary part, Chen prime,[13] and a strictly non-palindromic number.

317 is the exponent (and number of ones) in the fourth base-10 repunit prime.[14]

318 edit

Main article: 318 (number)

319 edit

319 = 11 × 29. 319 is the sum of three consecutive primes (103 + 107 + 109), Smith number,[15] cannot be represented as the sum of fewer than 19 fourth powers, happy number in base 10[16]

320s edit

320 edit

320 = 26 × 5 = (25) × (2 × 5). 320 is a Leyland number,[17] and maximum determinant of a 10 by 10 matrix of zeros and ones.

321 edit

321 = 3 × 107, a Delannoy number[18]

322 edit

322 = 2 × 7 × 23. 322 is a sphenic,[19] nontotient, untouchable,[4] and a Lucas number.[20]

323 edit

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

324 edit

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,[22] and an untouchable number.[4]

325 edit

325 = 52 × 13. 325 is a triangular number, hexagonal number,[23] nonagonal number,[24] centered nonagonal number.[25] 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 edit

326 = 2 × 163. 326 is a nontotient, noncototient,[26] and an untouchable number.[4] 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 edit

327 = 3 × 109. 327 is a perfect totient number,[27] number of compositions of 10 whose run-lengths are either weakly increasing or weakly decreasing[28]

328 edit

328 = 23 × 41. 328 is a refactorable number,[29] 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 edit

329 = 7 × 47. 329 is the sum of three consecutive primes (107 + 109 + 113), and a highly cototient number.[30]

330s edit

330 edit

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  ), a pentagonal number,[31] divisible by the number of primes below it, and a sparsely totient number.[32]

331 edit

331 is a prime number, super-prime, cuban prime,[33] sum of five consecutive primes (59 + 61 + 67 + 71 + 73), centered pentagonal number,[34] centered hexagonal number,[35] and Mertens function returns 0.[36]

332 edit

332 = 22 × 83, Mertens function returns 0.[36]

333 edit

333 = 32 × 37, Mertens function returns 0,[36]

334 edit

334 = 2 × 167, nontotient.[37]

335 edit

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

336 edit

336 = 24 × 3 × 7, untouchable number,[4] number of partitions of 41 into prime parts.[38]

337 edit

337, prime number, emirp, permutable prime with 373 and 733, Chen prime,[13] star number

338 edit

338 = 2 × 132, nontotient, number of square (0,1)-matrices without zero rows and with exactly 4 entries equal to 1.[39]

339 edit

339 = 3 × 113, Ulam number[40]

340s edit

340 edit

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.[26] 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 edit

341 = 11 × 31, sum of seven consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61), octagonal number,[41] centered cube number,[42] 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 "bm−1 − 1 is divisible by m", for bases up to 128 of b = 2, 15, 60, 63, 78, and 108.

342 edit

342 = 2 × 32 × 19, pronic number,[3] Untouchable number.[4]

343 edit

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 edit

344 = 23 × 43, octahedral number,[43] noncototient,[26] totient sum of the first 33 integers, refactorable number.[29]

345 edit

345 = 3 × 5 × 23, sphenic number,[19] idoneal number

346 edit

346 = 2 × 173, Smith number,[15] noncototient.[26]

347 edit

347 is a prime number, emirp, safe prime,[44] Eisenstein prime with no imaginary part, Chen prime,[13] Friedman prime since 347 = 73 + 4, and a strictly non-palindromic number.

348 edit

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

349 edit

349, prime number, sum of three consecutive primes (109 + 113 + 127), 5349 - 4349 is a prime number.[45]

350s edit

350 edit

350 = 2 × 52 × 7 =  , primitive semiperfect number,[46] divisible by the number of primes below it, nontotient, a truncated icosahedron of frequency 6 has 350 hexagonal faces and 12 pentagonal faces.

351 edit

351 = 33 × 13, triangular number, sum of five consecutive primes (61 + 67 + 71 + 73 + 79), member of Padovan sequence[47] and number of compositions of 15 into distinct parts.[48]

352 edit

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).

353 edit

Main article: 353 (number)

354 edit

354 = 2 × 3 × 59 = 14 + 24 + 34 + 44,[49][50] sphenic number,[19] nontotient, also SMTP code meaning start of mail input. It is also sum of absolute value of the coefficients of Conway's polynomial.

355 edit

355 = 5 × 71, Smith number,[15] Mertens function returns 0,[36] 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 edit

356 = 22 × 89, Mertens function returns 0.[36]

357 edit

357 = 3 × 7 × 17, sphenic number.[19]

358 edit

358 = 2 × 179, sum of six consecutive primes (47 + 53 + 59 + 61 + 67 + 71), Mertens function returns 0,[36] number of ways to partition {1,2,3,4,5} and then partition each cell (block) into subcells.[51]

359 edit

Main article: 359 (number)

360s edit

360 edit

Main article: 360 (number)

361 edit

361 = 192, centered triangular number,[11] centered octagonal number, centered decagonal number,[52] member of the Mian–Chowla sequence;[53] also the number of positions on a standard 19 x 19 Go board.

362 edit

362 = 2 × 181 = σ2(19): sum of squares of divisors of 19,[54] Mertens function returns 0,[36] nontotient, noncototient.[26]

363 edit

Main article: 363 (number)

364 edit

364 = 22 × 7 × 13, tetrahedral number,[55] sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), Mertens function returns 0,[36] 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.[56]

365 edit

Main article: 365 (number)

366 edit

366 = 2 × 3 × 61, sphenic number,[19] Mertens function returns 0,[36] noncototient,[26] number of complete partitions of 20,[57] 26-gonal and 123-gonal. Also the number of days in a Leap Year.

367 edit

367 is a prime number, Perrin number,[58] happy number, prime index prime and a strictly non-palindromic number.

368 edit

368 = 24 × 23. It is also a Leyland number.[17]

369 edit

Main article: 369 (number)

370s edit

370 edit

370 = 2 × 5 × 37, sphenic number,[19] 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 edit

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 edit

372 = 22 × 3 × 31, sum of eight consecutive primes (31 + 37 + 41 + 43 + 47 + 53 + 59 + 61), noncototient,[26] untouchable number,[4] refactorable number.[29]

373 edit

373, prime number, balanced prime,[59] 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 edit

374 = 2 × 11 × 17, sphenic number,[19] nontotient, 3744 + 1 is prime.[60]

375 edit

375 = 3 × 53, number of regions in regular 11-gon with all diagonals drawn.[61]

376 edit

376 = 23 × 47, pentagonal number,[31] 1-automorphic number,[62] nontotient, refactorable number.[29] There is a math puzzle in which when 376 is squared, 376 is also the last three digits, as 376 * 376 = 141376 [63]

377 edit

377 = 13 × 29, Fibonacci number, a centered octahedral number,[64] a Lucas and Fibonacci pseudoprime, the sum of the squares of the first six primes.

378 edit

378 = 2 × 33 × 7, triangular number, cake number, hexagonal number,[23] Smith number.[15]

379 edit

379 is a prime number, Chen prime,[13] 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.

380s edit

380 edit

380 = 22 × 5 × 19, pronic number,[3] 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 edit

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 edit

382 = 2 × 191, sum of ten consecutive primes (19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59), Smith number.[15]

383 edit

383, prime number, safe prime,[44] Woodall prime,[65] 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.[66] 4383 - 3383 is prime.

384 edit

Main article: 384 (number)

385 edit

385 = 5 × 7 × 11, sphenic number,[19] square pyramidal number,[67] the number of integer partitions of 18.

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

386 edit

386 = 2 × 193, nontotient, noncototient,[26] centered heptagonal number,[12] number of surface points on a cube with edge-length 9.[68]

387 edit

387 = 32 × 43, number of graphical partitions of 22.[69]

388 edit

388 = 22 × 97 = solution to postage stamp problem with 6 stamps and 6 denominations,[70] number of uniform rooted trees with 10 nodes.[71]

389 edit

389, prime number, emirp, Eisenstein prime with no imaginary part, Chen prime,[13] highly cototient number,[30] strictly non-palindromic number. Smallest conductor of a rank 2 Elliptic curve.

390s edit

390 edit

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

  is prime[72]

391 edit

391 = 17 × 23, Smith number,[15] centered pentagonal number.[34]

392 edit

392 = 23 × 72, Achilles number.

393 edit

393 = 3 × 131, Blum integer, Mertens function returns 0.[36]

394 edit

394 = 2 × 197 = S5 a Schröder number,[73] nontotient, noncototient.[26]

395 edit

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.[74]

396 edit

396 = 22 × 32 × 11, sum of twin primes (197 + 199), totient sum of the first 36 integers, refactorable number,[29] Harshad number, digit-reassembly number.

397 edit

397, prime number, cuban prime,[33] centered hexagonal number.[35]

398 edit

398 = 2 × 199, nontotient.

  is prime[72]

399 edit

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

References edit

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  50. ^ Sloane, N. J. A. (ed.). "Sequence A031971 (a(n) = Sum_{k=1..n} k^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  51. ^ Sloane, N. J. A. (ed.). "Sequence A000258 (Expansion of e.g.f. exp(exp(exp(x)-1)-1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  52. ^ Sloane, N. J. A. (ed.). "Sequence A062786 (Centered 10-gonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-22.
  53. ^ Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-22.
  54. ^ Sloane, N. J. A. (ed.). "Sequence A001157 (a(n) = sigma_2(n): sum of squares of divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  55. ^ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-22.
  56. ^ Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral (or triangular pyramidal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  57. ^ Sloane, N. J. A. (ed.). "Sequence A126796 (Number of complete partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  58. ^ Sloane, N. J. A. (ed.). "Sequence A001608 (Perrin sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-22.
  59. ^ Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-22.
  60. ^ Sloane, N. J. A. (ed.). "Sequence A000068 (Numbers k such that k^4 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  61. ^ Sloane, N. J. A. (ed.). "Sequence A007678 (Number of regions in regular n-gon with all diagonals drawn)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  62. ^ Sloane, N. J. A. (ed.). "Sequence A003226 (Automorphic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-22.
  63. ^ https://www.mathsisfun.com/puzzles/algebra-cow-solution.html
  64. ^ Sloane, N. J. A. (ed.). "Sequence A001845 (Centered octahedral numbers (crystal ball sequence for cubic lattice))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
  65. ^ Sloane, N. J. A. (ed.). "Sequence A050918 (Woodall primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-22.
  66. ^ Sloane, N. J. A. (ed.). "Sequence A072385 (Primes which can be represented as the sum of a prime and its reverse)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2019-06-02.
  67. ^ Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-22.
  68. ^ Sloane, N. J. A. (ed.). "Sequence A005897 (a(n) = 6*n^2 + 2 for n > 0, a(0)=1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  69. ^ Sloane, N. J. A. (ed.). "Sequence A000569 (Number of graphical partitions of 2n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  70. ^ Sloane, N. J. A. (ed.). "Sequence A084192 (Array read by antidiagonals: T(n,k) = solution to postage stamp problem with n stamps and k denominations (n >= 1, k >= 1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  71. ^ Sloane, N. J. A. (ed.). "Sequence A317712 (Number of uniform rooted trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  72. ^ a b Sloane, N. J. A. (ed.). "Sequence A162862 (Numbers n such that n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
  73. ^ Sloane, N. J. A. (ed.). "Sequence A006318 (Large Schröder numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-22.
  74. ^ Sloane, N. J. A. (ed.). "Sequence A002955 (Number of (unordered, unlabeled) rooted trimmed trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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