A023831 Sum of exponents in prime-power factorization of C(4n,n+1).

2, 4, 4, 7, 7, 8, 8, 11, 11, 12, 8, 12, 13, 15, 13, 18, 14, 18, 14, 18, 20, 18, 17, 21, 22, 20, 19, 22, 20, 24, 19, 26, 24, 26, 23, 28, 27, 27, 27, 30, 29, 31, 27, 30, 30, 30, 27, 34, 31, 33, 31, 34, 33, 33, 30, 34, 33, 36, 31, 37, 38, 39, 37, 42, 39, 41, 38, 42, 43, 43, 38, 46, 44, 44, 44, 46, 46

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A023826, A023827, A023828, A023829, A023830, A023832, A023833, A023834, A023835, A023836.

Programs

Mathematica

Table[PrimeOmega[Binomial[4 n, n + 1]], {n, 77}] (* Ivan Neretin, Nov 08 2017 *)

PARI

a(n) = bigomega(binomial(4*n,n+1)); \\ Amiram Eldar, Jun 13 2025

Formula

a(n) = A023826(n) - A001222(3*n) + A001222(n+1). - Amiram Eldar, Jun 13 2025