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

0,2

Links

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

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)

Mathematica

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

Prog

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

Crossrefs

Cf. A001222, A001448, A023816, A022559.

Sequence in context: A309560 A128054 A175081 * A084735 A002734 A367417

Adjacent sequences: A023831 A023832 A023833 * A023835 A023836 A023837

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved