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.

Previous Showing 11-13 of 13 results.

A023850 Sum of exponents in prime-power factorization of binomial(5n, 2n+1).

Original entry on oeis.org

2, 5, 5, 7, 9, 10, 11, 14, 13, 14, 14, 15, 17, 18, 19, 20, 19, 21, 18, 25, 26, 21, 24, 26, 25, 30, 28, 28, 31, 32, 31, 32, 32, 32, 33, 36, 34, 36, 38, 37, 37, 39, 33, 38, 40, 37, 39, 41, 40, 43, 43, 46, 49, 47, 47, 50, 46, 50, 47, 52, 52, 52, 52, 51, 53, 53, 48, 53, 57, 53, 57, 58, 56, 59, 58, 60
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A001222, A023837, A023839, A023840, A023841, A023842, A023843, A023844, A023845, A023846, A023847, A023848, A023849, A023851.

Programs

  • Mathematica
    Table[PrimeOmega[Binomial[5 n, 2 n + 1]], {n, 76}] (* Ivan Neretin, Nov 09 2017 *)
  • PARI
    a(n) = bigomega(binomial(5*n,2*n+1)); \\ Amiram Eldar, Jun 14 2025

Formula

a(n) = A023847(n) + A001222(3*n) - A001222(2*n+1). - Amiram Eldar, Jun 14 2025

A023851 Sum of exponents in prime-power factorization of binomial(5n, 2n+2).

Original entry on oeis.org

1, 4, 5, 6, 8, 9, 10, 12, 12, 13, 15, 15, 16, 16, 17, 19, 18, 20, 18, 23, 25, 21, 22, 24, 24, 28, 29, 27, 29, 31, 28, 31, 32, 30, 32, 35, 34, 34, 36, 37, 35, 40, 36, 35, 39, 36, 37, 40, 38, 41, 43, 46, 46, 46, 45, 48, 46, 49, 47, 51, 52, 50, 48, 49, 51, 52, 49, 52, 55, 53, 54, 58, 55, 57, 60, 58, 62
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A001222, A023837, A023839, A023840, A023841, A023842, A023843, A023844, A023845, A023846, A023847, A023848, A023849, A023851.

Programs

  • Mathematica
    Table[PrimeOmega[Binomial[5 n, 2 n + 2]], {n, 77}] (* Ivan Neretin, Nov 09 2017 *)
  • PARI
    a(n) = bigomega(binomial(5*n,2*n+2)); \\ Amiram Eldar, Jun 14 2025

Formula

a(n) = A023850(n) + A001222(3*n-1) - A001222(2*n+2). - Amiram Eldar, Jun 14 2025

Extensions

Missing terms a(31), a(32) fixed by Ivan Neretin, Nov 09 2017

A023838 Sum of exponents in prime-power factorization of C(5n,n-1).

Original entry on oeis.org

0, 2, 3, 5, 5, 7, 8, 9, 8, 10, 10, 12, 14, 13, 15, 14, 14, 16, 14, 17, 17, 18, 18, 21, 18, 22, 24, 23, 23, 24, 24, 24, 23, 23, 24, 25, 24, 26, 28, 29, 25, 30, 27, 29, 33, 30, 30, 32, 32, 33, 33, 37, 37, 38, 38, 37, 36, 40, 39, 44, 39, 41, 40, 39, 37, 39, 38, 39, 42, 41, 44, 44, 43, 43, 44, 46, 48, 49
Offset: 1

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A001222, A004343, A023837, A023839, A023840, A023841, A023842, A023843, A023844, A023845, A023846, A023847, A023848, A023849, A023850, A023851.

Programs

  • Mathematica
    Join[{0},Table[Total[Transpose[FactorInteger[Binomial[5 n,n-1]]] [[2]]],{n,2,80}]] (* Harvey P. Dale, Dec 31 2012 *)
a[n_] := PrimeOmega[Binomial[5*n, n-1]]; Array[a, 100] (* Amiram Eldar, Jun 14 2025 *)
  • PARI
    a(n) = bigomega(binomial(5*n,n-1)); \\ Amiram Eldar, Jun 14 2025

Formula

From Amiram Eldar, Jun 14 2025: (Start)
a(n) = A001222(A004343(n)).
a(n) = A023837(n) - A001222(4*n+1) + A001222(n). (End)
Previous Showing 11-13 of 13 results.

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

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