# 300 (number)

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
Hebrewש
ArmenianՅ
Babylonian cuneiform𒐙
Egyptian hieroglyph𓍤

## 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 22 × 3 × 52. 30064 + 1 is prime

## Integers from 301 to 399

### 300s

#### 309

309 = 3 × 103, Blum integer, number of primes <= 211.[1]

### 310s

#### 312

312 = 23 × 3 × 13, idoneal number.

#### 314

314 = 2 × 157. 314 is a nontotient,[2] smallest composite number in Somos-4 sequence.[3]

#### 315

315 = 32 × 5 × 7 = ${\displaystyle D_{7,3}\!}$  rencontres number, highly composite odd number, having 12 divisors.[4]

#### 316

316 = 22 × 79, a centered triangular number[5] and a centered heptagonal number.[6]

#### 317

317 is a prime number, Eisenstein prime with no imaginary part, Chen prime,[7] one of the rare primes to be both right and left-truncatable,[8] and a strictly non-palindromic number.

317 is the exponent (and number of ones) in the fourth base-10 repunit prime.[9]

#### 319

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

### 320s

#### 320

320 = 26 × 5 = (25) × (2 × 5). 320 is a Leyland number,[12] and maximum determinant of a 10 by 10 matrix of zeros and ones.

#### 321

321 = 3 × 107, a Delannoy number[13]

#### 322

322 = 2 × 7 × 23. 322 is a sphenic,[14] nontotient, untouchable,[15] and a Lucas number.[16]

#### 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.[17] 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,[18] and an untouchable number.[15]

#### 325

325 = 52 × 13. 325 is a triangular number, hexagonal number,[19] nonagonal number,[20] centered nonagonal number.[21] 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,[22] and an untouchable number.[15] 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[23]

#### 327

327 = 3 × 109. 327 is a perfect totient number,[24] number of compositions of 10 whose run-lengths are either weakly increasing or weakly decreasing[25]

#### 328

328 = 23 × 41. 328 is a refactorable number,[26] 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.[27]

### 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 ${\displaystyle {\tbinom {11}{4}}}$ ), a pentagonal number,[28] divisible by the number of primes below it, and a sparsely totient number.[29]

#### 331

331 is a prime number, super-prime, cuban prime,[30] a lucky prime,[31] sum of five consecutive primes (59 + 61 + 67 + 71 + 73), centered pentagonal number,[32] centered hexagonal number,[33] and Mertens function returns 0.[34]

#### 332

332 = 22 × 83, Mertens function returns 0.[34]

#### 333

333 = 32 × 37, Mertens function returns 0;[34] repdigit; 2333 is the smallest power of two greater than a googol.

#### 334

334 = 2 × 167, nontotient.[35]

#### 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,[15] number of partitions of 41 into prime parts.[36]

#### 337

337, prime number, emirp, permutable prime with 373 and 733, Chen prime,[7] star number

#### 338

338 = 2 × 132, nontotient, number of square (0,1)-matrices without zero rows and with exactly 4 entries equal to 1.[37]

#### 339

339 = 3 × 113, Ulam number[38]

### 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.[22] 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

341 = 11 × 31, sum of seven consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61), octagonal number,[39] centered cube number,[40] 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,[41] Untouchable number.[15]

#### 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,[42] noncototient,[22] totient sum of the first 33 integers, refactorable number.[26]

#### 345

345 = 3 × 5 × 23, sphenic number,[14] idoneal number

#### 346

346 = 2 × 173, Smith number,[10] noncototient.[22]

#### 347

347 is a prime number, emirp, safe prime,[43] Eisenstein prime with no imaginary part, Chen prime,[7] Friedman prime since 347 = 73 + 4, twin prime with 349, and a strictly non-palindromic number.

#### 348

348 = 22 × 3 × 29, sum of four consecutive primes (79 + 83 + 89 + 97), refactorable number.[26]

#### 349

349, prime number, sum of three consecutive primes (109 + 113 + 127), 5349 - 4349, [44] is a prime number.

### 350s

#### 350

350 = 2 × 52 × 7 = ${\displaystyle \left\{{7 \atop 4}\right\}}$ , primitive semiperfect number,[45] 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[46] and number of compositions of 15 into distinct parts.[47]

#### 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[23]

#### 354

354 = 2 × 3 × 59 = 14 + 24 + 34 + 44,[48][49] sphenic number,[14] 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,[10] Mertens function returns 0,[34] 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.[34]

#### 357

357 = 3 × 7 × 17, sphenic number.[14]

#### 358

358 = 2 × 179, sum of six consecutive primes (47 + 53 + 59 + 61 + 67 + 71), Mertens function returns 0,[34] number of ways to partition {1,2,3,4,5} and then partition each cell (block) into subcells.[50]

### 360s

#### 361

361 = 192. 361 is a centered triangular number,[5] centered octagonal number, centered decagonal number,[51] member of the Mian–Chowla sequence;[52] 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,[53] Mertens function returns 0,[34] nontotient, noncototient.[22]

#### 364

364 = 22 × 7 × 13, tetrahedral number,[54] sum of twelve consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53), Mertens function returns 0,[34] 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.[54]

#### 366

366 = 2 × 3 × 61, sphenic number,[14] Mertens function returns 0,[34] noncototient,[22] number of complete partitions of 20,[55] 26-gonal and 123-gonal. Also the number of days in a leap year.

#### 367

367 is a prime number, a lucky prime,[31] Perrin number,[56] happy number, prime index prime and a strictly non-palindromic number.

#### 368

368 = 24 × 23. It is also a Leyland number.[12]

### 370s

#### 370

370 = 2 × 5 × 37, sphenic number,[14] 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,[57] 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,[22] untouchable number,[15] --> refactorable number.[26]

#### 373

373, prime number, balanced prime,[58] one of the rare primes to be both right and left-truncatable (two-sided prime),[8] 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. Also a sexy prime with 367 and 379.

#### 374

374 = 2 × 11 × 17, sphenic number,[14] nontotient, 3744 + 1 is prime.[59]

#### 375

375 = 3 × 53, number of regions in regular 11-gon with all diagonals drawn.[60]

#### 376

376 = 23 × 47, pentagonal number,[28] 1-automorphic number,[61] nontotient, refactorable number.[26] There is a math puzzle in which when 376 is squared, 376 is also the last three digits, as 376 * 376 = 141376 [62]

#### 377

377 = 13 × 29, Fibonacci number, a centered octahedral number,[63] 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,[19] Smith number.[10]

#### 379

379 is a prime number, Chen prime,[7] lazy caterer number[23] 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,[41] 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.[64]

#### 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.[10]

#### 383

383, prime number, safe prime,[43] 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.

#### 385

385 = 5 × 7 × 11, sphenic number,[14] 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,[22] centered heptagonal number,[6] 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,[7] highly cototient number,[27] 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,

${\displaystyle \sum _{n=0}^{10}{390}^{n}}$  is prime[72]

#### 391

391 = 17 × 23, Smith number,[10] centered pentagonal number.[32]

#### 392

392 = 23 × 72, Achilles number.

#### 393

393 = 3 × 131, Blum integer, Mertens function returns 0.[34]

#### 394

394 = 2 × 197 = S5 a Schröder number,[73] nontotient, noncototient.[22]

#### 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,[26] Harshad number, digit-reassembly number.

#### 397

397, prime number, cuban prime,[30] centered hexagonal number.[33]

#### 398

398 = 2 × 199, nontotient.

${\displaystyle \sum _{n=0}^{10}{398}^{n}}$  is prime[72]

#### 399

399 = 3 × 7 × 19, sphenic number,[14] smallest Lucas–Carmichael number, Leyland number of the second kind. 399! + 1 is prime.

## References

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3. ^ Sloane, N. J. A. (ed.). "Sequence A006720 (Somos-4 sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
4. ^
5. ^ a b Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
6. ^ a b Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
7. Sloane, N. J. A. (ed.). "Sequence A109611 (Chen primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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9. ^ Guy, Richard; Unsolved Problems in Number Theory, p. 7 ISBN 1475717385
10. Sloane, N. J. A. (ed.). "Sequence A006753 (Smith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
11. ^
12. ^ a b Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
13. ^ Sloane, N. J. A. (ed.). "Sequence A001850 (Central Delannoy numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
14. Sloane, N. J. A. (ed.). "Sequence A007304 (Sphenic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
15. ^ Sloane, N. J. A. (ed.). "Sequence A000032 (Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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20. ^ Sloane, N. J. A. (ed.). "Sequence A060544 (Centered 9-gonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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22. ^ a b c
23. ^ Sloane, N. J. A. (ed.). "Sequence A082897 (Perfect totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
24. ^
25. Sloane, N. J. A. (ed.). "Sequence A033950 (Refactorable numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
26. ^ a b Sloane, N. J. A. (ed.). "Sequence A100827 (Highly cototient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
27. ^ a b Sloane, N. J. A. (ed.). "Sequence A000326 (Pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
28. ^ Sloane, N. J. A. (ed.). "Sequence A036913 (Sparsely totient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
29. ^ a b
30. ^ a b Sloane, N. J. A. (ed.). "Sequence A031157 (Numbers that are both lucky and prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
31. ^ a b Sloane, N. J. A. (ed.). "Sequence A005891 (Centered pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
32. ^ a b Sloane, N. J. A. (ed.). "Sequence A003215 (Hex numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
33. Sloane, N. J. A. (ed.). "Sequence A028442 (Numbers n such that Mertens' function is zero)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
34. ^ Sloane, N. J. A. (ed.). "Sequence A003052 (Self numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
35. ^ Sloane, N. J. A. (ed.). "Sequence A000607 (Number of partitions of n into prime parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
36. ^
37. ^ Sloane, N. J. A. (ed.). "Sequence A002858 (Ulam numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
38. ^ Sloane, N. J. A. (ed.). "Sequence A000567 (Octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
39. ^ Sloane, N. J. A. (ed.). "Sequence A005898 (Centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
40. ^ a b {{cite OEIS|A002378|2=Oblong (or promic, pronic, or heteromecic) numbers: a(n) = n*(n+1)
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43. ^ Sloane, N. J. A. (ed.). "Sequence A059802 (Numbers k such that 5^k - 4^k is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
44. ^ Sloane, N. J. A. (ed.). "Sequence A006036 (Primitive pseudoperfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
45. ^ Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
46. ^
47. ^ Sloane, N. J. A. (ed.). "Sequence A000538 (Sum of fourth powers: 0^4 + 1^4 + ... + n^4)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
48. ^ Sloane, N. J. A. (ed.). "Sequence A031971 (a(n) = Sum_{k=1..n} k^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
49. ^ 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.
50. ^ Sloane, N. J. A. (ed.). "Sequence A062786 (Centered 10-gonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
51. ^ Sloane, N. J. A. (ed.). "Sequence A005282 (Mian-Chowla sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
52. ^ 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.
53. ^ a b Sloane, N. J. A. (ed.). "Sequence A000292 (Tetrahedral numbers (or triangular pyramidal))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
54. ^ Sloane, N. J. A. (ed.). "Sequence A126796 (Number of complete partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
55. ^ Sloane, N. J. A. (ed.). "Sequence A001608 (Perrin sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
56. ^
57. ^ Sloane, N. J. A. (ed.). "Sequence A006562 (Balanced primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
58. ^ 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.
59. ^
60. ^ Sloane, N. J. A. (ed.). "Sequence A003226 (Automorphic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
61. ^ "Algebra COW Puzzle - Solution". Archived from the original on 2023-10-19. Retrieved 2023-09-21.
62. ^
63. ^
64. ^ Sloane, N. J. A. (ed.). "Sequence A050918 (Woodall primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
65. ^
66. ^ Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
67. ^ 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.
68. ^ Sloane, N. J. A. (ed.). "Sequence A000569 (Number of graphical partitions of 2n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
69. ^
70. ^ Sloane, N. J. A. (ed.). "Sequence A317712 (Number of uniform rooted trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
71. ^ a b
72. ^ Sloane, N. J. A. (ed.). "Sequence A006318 (Large Schröder numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
73. ^