A023816 Sum of exponents in prime-power factorization of C(2n,n).

0, 1, 2, 3, 3, 5, 5, 6, 6, 6, 6, 8, 7, 9, 11, 11, 9, 11, 11, 12, 12, 12, 12, 15, 13, 14, 15, 14, 14, 16, 15, 16, 15, 16, 16, 17, 15, 16, 18, 19, 17, 21, 20, 22, 22, 21, 22, 24, 22, 22, 23, 23, 22, 25, 23, 23, 22, 22, 23, 26, 25, 27, 28, 29, 25, 26, 25, 27, 29, 29, 28, 30, 28, 30, 32, 31, 30, 32, 32, 33

Offset

0,3

Links

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

Formula

From Amiram Eldar, Jun 11 2025: (Start)

a(n) = A001222(A000984(n)).

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

Maple

with(numtheory):a:=proc(n) if n=0 then 0 else bigomega(binomial(2*n, n)) fi end: seq(a(n), n=0..79); # Zerinvary Lajos, Apr 11 2008

Mathematica

Join[{0}, Table[Total[FactorInteger[Binomial[2 n, n]][[All, 2]]], {n, 79}]] (* Ivan Neretin, Oct 26 2017 *)

Prog

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

Crossrefs

Cf. A000984, A001222, A022559.

Sequence in context: A262488 A278530 A330332 * A353714 A159237 A335599

Adjacent sequences: A023813 A023814 A023815 * A023817 A023818 A023819

Keyword

nonn

Author

Clark Kimberling

Extensions

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

Status

approved