Английская Википедия:300 (number)

Материал из Онлайн справочника
Перейти к навигацииПерейти к поиску

Шаблон:More citations needed Шаблон:Infobox number

300 (three hundred) is the natural number following 299 and preceding 301. Шаблон:TOC limit

Mathematical properties

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 Шаблон:Nowrap 30064 + 1 is prime

Integers from 301 to 399

300s

301

Шаблон:Main

302

Шаблон:Main

303

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

304

Шаблон:Main

305

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

306

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

Шаблон:Main

308

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

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

310s

310

Шаблон:Main

311

Шаблон:Main

312

Шаблон:Main 312 = 23 × 3 × 13, idoneal number.

313

Шаблон:Main

314

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

315

315 = 32 × 5 × 7 = <math>D_{7,3} \!</math> rencontres number, highly composite odd number, having 12 divisors.[10]

316

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

317

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

Шаблон:Main

319

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

320

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

321 = 3 × 107, a Delannoy number[18]

322

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

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

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

325

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

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 Шаблон:OEIS.

327

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

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

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

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 <math>\tbinom {11}4 </math>), a pentagonal number,[31] divisible by the number of primes below it, and a sparsely totient number.[32]

331

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

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

333

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

334

334 = 2 × 167, nontotient.[37]

335

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

336

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

337

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

338

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

339

339 = 3 × 113, Ulam number[40]

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.[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 Шаблон:OEIS and Шаблон:OEIS.

341

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

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

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,[43] noncototient,[26] totient sum of the first 33 integers, refactorable number.[29]

345

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

346

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

347

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

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

349

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

350s

350

350 = 2 × 52 × 7 = <math>\left\{ {7 \atop 4} \right\}</math>, 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

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

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 Шаблон:OEIS.

353

Шаблон:Main

354

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

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

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

357

357 = 3 × 7 × 17, sphenic number.[19]

358

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

Шаблон:Main

360s

360

Шаблон:Main

361

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

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

363

Шаблон:Main

364

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

Шаблон:Main

366

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

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

368

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

369

Шаблон:Main

370s

370

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

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 Шаблон:OEIS, 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,[26] untouchable number,[4] refactorable number.[29]

373

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

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

375

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

376

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

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

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

379

379 is a prime number, Chen prime,[13] lazy caterer number Шаблон: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

380

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 Шаблон:Oeis and Шаблон:Oeis.

381

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

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

383

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

Шаблон:Main

385

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

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

387

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

388

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

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

390

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

<math>\sum_{n=0}^{10}{390}^{n}</math> is prime[72]

391

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

392

392 = 23 × 72, Achilles number.

393

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

394

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

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.[74]

396

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

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

398

398 = 2 × 199, nontotient.

<math>\sum_{n=0}^{10}{398}^{n}</math> is prime[72]

399

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

References

Шаблон:Reflist Шаблон:Integers

Партнерские ресурсы
Криптовалюты
Магазины
Хостинг
Разное

  1. ↑ Шаблон:Cite OEIS
  2. ↑ Шаблон:Cite OEIS
  3. ↑ 3,0 3,1 3,2 Шаблон:Cite OEIS
  4. ↑ 4,0 4,1 4,2 4,3 4,4 4,5 4,6 Шаблон:Cite OEIS
  5. ↑ {{Cite OEIS|A005277|Nontotients: even numbers k such that phi(m) = k has no solution
  6. ↑ Шаблон:Cite OEIS
  7. ↑ Шаблон:Cite OEIS
  8. ↑ {{Cite OEIS|A005277|Nontotients: even numbers k such that phi(m) = k has no solution
  9. ↑ Шаблон:Cite OEIS
  10. ↑ Шаблон:Cite web
  11. ↑ 11,0 11,1 Шаблон:Cite OEIS
  12. ↑ 12,0 12,1 Шаблон:Cite OEIS
  13. ↑ 13,0 13,1 13,2 13,3 13,4 Шаблон:Cite OEIS
  14. ↑ Guy, Richard; Unsolved Problems in Number Theory, p. 7 Шаблон:ISBN
  15. ↑ 15,0 15,1 15,2 15,3 15,4 15,5 Шаблон:Cite OEIS
  16. ↑ Шаблон:Cite OEIS
  17. ↑ 17,0 17,1 Шаблон:Cite OEIS
  18. ↑ Шаблон:Cite OEIS
  19. ↑ 19,0 19,1 19,2 19,3 19,4 19,5 19,6 19,7 19,8 Шаблон:Cite OEIS
  20. ↑ Шаблон:Cite OEIS
  21. ↑ Шаблон:Cite OEIS
  22. ↑ Шаблон:Cite web
  23. ↑ 23,0 23,1 Шаблон:Cite OEIS
  24. ↑ Шаблон:Cite OEIS
  25. ↑ Шаблон:Cite OEIS
  26. ↑ 26,0 26,1 26,2 26,3 26,4 26,5 26,6 26,7 26,8 Шаблон:Cite OEIS
  27. ↑ Шаблон:Cite OEIS
  28. ↑ Шаблон:Cite OEIS
  29. ↑ 29,0 29,1 29,2 29,3 29,4 29,5 Шаблон:Cite OEIS
  30. ↑ 30,0 30,1 Шаблон:Cite OEIS
  31. ↑ 31,0 31,1 Шаблон:Cite OEIS
  32. ↑ Шаблон:Cite OEIS
  33. ↑ 33,0 33,1 Шаблон:Cite OEIS
  34. ↑ 34,0 34,1 Шаблон:Cite OEIS
  35. ↑ 35,0 35,1 Шаблон:Cite OEIS
  36. ↑ 36,0 36,1 36,2 36,3 36,4 36,5 36,6 36,7 36,8 36,9 Шаблон:Cite OEIS
  37. ↑ Шаблон:Cite OEIS
  38. ↑ Шаблон:Cite OEIS
  39. ↑ Шаблон:Cite OEIS
  40. ↑ Шаблон:Cite OEIS
  41. ↑ Шаблон:Cite OEIS
  42. ↑ Шаблон:Cite OEIS
  43. ↑ Шаблон:Cite OEIS
  44. ↑ 44,0 44,1 Шаблон:Cite OEIS
  45. ↑ Шаблон:Cite OEIS
  46. ↑ Шаблон:Cite OEIS
  47. ↑ Шаблон:Cite OEIS
  48. ↑ Шаблон:Cite OEIS
  49. ↑ Шаблон:Cite OEIS
  50. ↑ Шаблон:Cite OEIS
  51. ↑ Шаблон:Cite OEIS
  52. ↑ Шаблон:Cite OEIS
  53. ↑ Шаблон:Cite OEIS
  54. ↑ Шаблон:Cite OEIS
  55. ↑ Шаблон:Cite OEIS
  56. ↑ Шаблон:Cite OEIS
  57. ↑ Шаблон:Cite OEIS
  58. ↑ Шаблон:Cite OEIS
  59. ↑ Шаблон:Cite OEIS
  60. ↑ Шаблон:Cite OEIS
  61. ↑ Шаблон:Cite OEIS
  62. ↑ Шаблон:Cite OEIS
  63. ↑ https://www.mathsisfun.com/puzzles/algebra-cow-solution.html
  64. ↑ Шаблон:Cite OEIS
  65. ↑ Шаблон:Cite OEIS
  66. ↑ Шаблон:Cite OEIS
  67. ↑ Шаблон:Cite OEIS
  68. ↑ Шаблон:Cite OEIS
  69. ↑ Шаблон:Cite OEIS
  70. ↑ Шаблон:Cite OEIS
  71. ↑ Шаблон:Cite OEIS
  72. ↑ 72,0 72,1 Шаблон:Cite OEIS
  73. ↑ Шаблон:Cite OEIS
  74. ↑ Шаблон:Cite OEIS
Источник — http://wikihandbk.com/ruwiki/index.php?title=Английская_Википедия:300_(number)&oldid=12845568