A023834 Sum of exponents in prime-power factorization of C(4n,2n).

0, 2, 3, 5, 6, 6, 7, 11, 9, 11, 12, 12, 13, 15, 14, 15, 15, 16, 15, 18, 17, 20, 22, 22, 22, 23, 22, 23, 22, 23, 25, 28, 25, 25, 29, 28, 28, 32, 30, 32, 31, 30, 31, 34, 34, 34, 34, 36, 35, 37, 34, 36, 38, 38, 38, 40, 38, 41, 42, 42, 40, 44, 46, 44, 43, 43, 44, 46, 42, 46, 47, 47, 46, 48, 47, 50, 51, 50

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A001222, A001448, A023816, A022559.

Programs

Mathematica

Join[{0}, Table[Total[FactorInteger[Binomial[4 n, 2 n]][[All, 2]]], {n, 77}]] (* Ivan Neretin, Oct 26 2017 *)

PARI

a(n) = bigomega(binomial(4*n, 2*n)); \\ Amiram Eldar, Jun 11 2025

Formula

From Amiram Eldar, Jun 11 2025: (Start)

a(n) = A001222(A001448(n)).

a(n) = A023816(2*n).

a(n) = A022559(4*n) - 2*A022559(2*n). (End)

Extensions

Offset changed to 0 and a(0) prepended by Amiram Eldar, Jun 11 2025