cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A382132 Centered pentagonal numbers which are semiprimes.

Original entry on oeis.org

6, 51, 106, 141, 226, 391, 526, 681, 766, 951, 1501, 1891, 2031, 2326, 2481, 2641, 3151, 3901, 4101, 4306, 6631, 6891, 7981, 8266, 8851, 10081, 10401, 11391, 13141, 14631, 15406, 16201, 20931, 22801, 23281, 24751, 27301, 27826, 28891, 29431, 30526, 32206, 33351, 35701, 36301, 38131, 38751
Offset: 1

Views

Author

Massimo Kofler, Mar 17 2025

Keywords

Examples

			A005891(1) = 6 = (5*1^2 + 5*1 + 2)/2 = 2*3.
A005891(4) = 51 = (5*4^2 + 5*4 + 2)/2 = 3*17.
A005891(6) = 106 = (5*6^2 + 5*6 + 2)/2 = 2*53.

Crossrefs

Intersection of A001358 and A005891.
Cf. A364610.

Programs

  • Mathematica
    Select[Table[(5*n^2 + 5*n + 2)/2, {n, 1, 125}], PrimeOmega[#] == 2 &] (* Amiram Eldar, Mar 17 2025 *)

A381043 Centered pentagonal numbers which are squarefree semiprimes.

Original entry on oeis.org

6, 51, 106, 141, 226, 391, 526, 681, 766, 951, 1501, 1891, 2031, 2326, 2481, 2641, 3151, 3901, 4101, 4306, 6631, 6891, 7981, 8266, 8851, 10081, 10401, 11391, 13141, 14631, 15406, 16201, 20931, 23281, 24751, 27301, 27826, 28891, 29431, 30526, 32206, 33351, 35701, 36301, 38131, 38751, 41926
Offset: 1

Views

Author

Massimo Kofler, Apr 14 2025

Keywords

Comments

Numbers such as 22801=151^2 and 1666681=1291^2 are in A382132 but not here.

Examples

			A005891(1) = 6 = (5*1^2 + 5*1 + 2)/2 = 2*3.
A005891(4) = 51 = (5*4^2 + 5*4 + 2)/2 = 3*17.
A005891(6) = 106 = (5*6^2 + 5*6 + 2)/2 = 2*53.

Crossrefs

Intersection of A006881 and A005891.
Cf. A145838, A382132, A364610.

Programs

  • Mathematica
    Select[Table[5*n*(n + 1)/2 + 1, {n, 0, 150}], FactorInteger[#][[;; , 2]] == {1, 1} &] (* Amiram Eldar, Apr 14 2025 *)

A382451 Centered pentagonal numbers which are the products of four distinct primes.

Original entry on oeis.org

5406, 12426, 20026, 23766, 40641, 55131, 83266, 115026, 118266, 136306, 142206, 145806, 176226, 184281, 205206, 209526, 245706, 279726, 284766, 315951, 326706, 371526, 387106, 407031, 413106, 419226, 425391, 498406, 505126, 553426, 623751, 638826, 672106, 685131
Offset: 1

Views

Author

Massimo Kofler, Mar 26 2025

Keywords

Examples

			A005891(46) = 5406 = (5*46^2 + 5*46 + 2)/2 = 2*3*17*53.
A005891(70) = 12426 = (5*70^2 + 5*70 + 2)/2 = 2*3*19*109.
A005891(127) = 40641 = (5*127^2 + 5*127 + 2)/2 = 3*19*23*31.

Crossrefs

Intersection of A005891 and A046386.
Cf. A364610.

Programs

  • Mathematica
    Select[Table[5*n*(n+1)/2+1, {n, 0, 600}], FactorInteger[#][[;; , 2]] == {1, 1, 1, 1} &] (* Amiram Eldar, Mar 26 2025 *)
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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