A023832 Sum of exponents in prime-power factorization of C(4n,n+2).

2, 3, 6, 6, 8, 6, 9, 10, 12, 10, 12, 12, 13, 12, 15, 16, 16, 16, 16, 17, 21, 16, 18, 20, 21, 19, 23, 20, 21, 20, 20, 26, 25, 23, 26, 27, 28, 24, 29, 29, 30, 31, 31, 29, 31, 26, 29, 33, 31, 31, 34, 32, 33, 31, 31, 33, 35, 33, 35, 36, 38, 35, 38, 40, 40, 39, 41, 41, 44, 40, 40, 46, 43, 43, 48, 44, 48

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001222, A023826, A023827, A023828, A023829, A023830, A023831, A023833, A023834, A023835, A023836.

Programs

Mathematica

Table[Total[Transpose[FactorInteger[Binomial[4n,n+2]]][[2]]],{n,80}] (* Harvey P. Dale, Jun 01 2014 *)
a[n_] := PrimeOmega[Binomial[4*n, n+2]]; Array[a, 100] (* Amiram Eldar, Jun 13 2025 *)

PARI

a(n) = bigomega(binomial(4*n,n+2)); \\ Amiram Eldar, Jun 13 2025

Formula

a(n) = A023831(n) - A001222(3*n-1) + A001222(n+2). - Amiram Eldar, Jun 13 2025