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 1-2 of 2 results.

A023854 Sum of exponents in prime-power factorization of binomial(6n, 3n).

Original entry on oeis.org

0, 3, 5, 6, 7, 11, 11, 12, 13, 14, 15, 16, 15, 19, 20, 21, 22, 23, 23, 22, 25, 29, 25, 29, 28, 31, 32, 30, 31, 34, 34, 35, 35, 36, 36, 38, 38, 41, 41, 41, 40, 46, 44, 43, 44, 44, 46, 47, 46, 47, 50, 51, 49, 53, 49, 52, 53, 53, 56, 55, 56, 60, 60, 61, 57, 61, 61, 61, 65, 66, 63, 67, 66, 69, 69, 66, 69, 71, 70, 72, 72
Offset: 0

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A001222, A022559, A023852, A023853, A066802.

Programs

  • Mathematica
    Join[{0}, Total[Transpose[FactorInteger[Binomial[6 #, 3 #]]][[2]]]&/@Range[80]] (* Harvey P. Dale, May 14 2011 *)
a[n_] := PrimeOmega[Binomial[6*n, 3*n]]; Array[a, 100, 0] (* Amiram Eldar, Jun 11 2025 *)
  • PARI
    a(n) = bigomega(binomial(6*n, 3*n)); \\ Amiram Eldar, Jun 11 2025

Formula

From Amiram Eldar, Jun 11 2025: (Start)
a(n) = A001222(A066802(n)).
a(n) = A022559(6*n) - 2*A022559(3*n). (End)

Extensions

Corrected and extended by Harvey P. Dale, May 14 2011
a(0)=0 inserted by Amiram Eldar, Jun 11 2025

A023852 Sum of exponents in prime-power factorization of binomial(6n, n).

Original entry on oeis.org

0, 2, 3, 6, 5, 7, 9, 9, 8, 10, 10, 14, 13, 12, 15, 16, 15, 16, 16, 19, 16, 18, 22, 24, 22, 23, 21, 23, 22, 22, 24, 25, 25, 24, 25, 28, 25, 27, 28, 28, 26, 31, 30, 38, 36, 33, 38, 38, 37, 35, 36, 38, 33, 33, 37, 38, 36, 39, 37, 43, 39, 41, 43, 46, 42, 40, 41, 45, 46, 43, 47, 46, 45, 46, 47, 49, 47, 45
Offset: 0

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A001222, A004355, A022559.
Cf. A023853, A023854.

Programs

  • Maple
    with(numtheory):a:=proc(n) if n=0 then 0 else bigomega(binomial(6*n,n)) fi end: seq(a(n), n=0..77); # Zerinvary Lajos, Apr 11 2008
  • Mathematica
    Table[PrimeOmega[Binomial[6 n, n]], {n, 0, 77}] (* Ivan Neretin, Nov 09 2017 *)
  • PARI
    a(n) = bigomega(binomial(6*n, n)); \\ Michel Marcus, Nov 10 2017

Formula

a(n) = A001222(A004355(n)). - Michel Marcus, Nov 10 2017
a(n) = A022559(6*n) - A022559(5*n) - A022559(n). - Amiram Eldar, Jun 11 2025

Extensions

a(0)=0 inserted by Amiram Eldar, Jun 11 2025
Showing 1-2 of 2 results.

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