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

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

Author

Clark Kimberling

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 0..10000

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