A023833 Sum of exponents in prime-power factorization of C(4n,n+3).

0, 4, 5, 7, 6, 8, 8, 11, 11, 12, 11, 12, 10, 15, 13, 17, 15, 17, 16, 18, 18, 20, 17, 20, 19, 21, 21, 21, 18, 22, 20, 26, 22, 26, 25, 27, 25, 28, 28, 30, 29, 31, 30, 31, 28, 28, 27, 33, 30, 33, 31, 33, 30, 35, 30, 34, 33, 35, 36, 35, 33, 37, 37, 42, 38, 41, 39, 42, 41, 44, 39, 45, 42, 45, 46, 45, 44

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, A023831, A023832, A023834, A023835, A023836.

Programs

Mathematica

Join[{0},Total[Transpose[FactorInteger[#]][[2]]]&/@Table[Binomial[4n,n+3],{n,2,80}]] (* Harvey P. Dale, Dec 24 2014 *)
a[n_] := PrimeOmega[Binomial[4*n, n+3]]; Array[a, 100] (* Amiram Eldar, Jun 13 2025 *)

PARI

a(n) = bigomega(binomial(4*n,n+3)); \\ Amiram Eldar, Jun 13 2025

Formula

a(n) = A023832(n) - A001222(3*n-2) + A001222(n+3). - Amiram Eldar, Jun 13 2025