A023818 Sum of exponents in prime-power factorization of C(2n,n-2).

0, 2, 3, 5, 4, 4, 6, 8, 6, 7, 8, 9, 8, 10, 11, 12, 11, 11, 12, 14, 11, 12, 14, 15, 13, 15, 16, 16, 13, 13, 17, 19, 14, 16, 18, 17, 15, 18, 19, 22, 20, 20, 21, 24, 21, 20, 23, 24, 23, 24, 22, 23, 22, 23, 24, 25, 22, 24, 27, 27, 22, 26, 29, 30, 26, 26, 28, 30, 27, 28, 31, 31, 29, 31, 31, 33, 31, 28, 31

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A001222, A002694, A023816, A023817.

Programs

Mathematica

Join[{0}, Table[Total[FactorInteger[Binomial[2 n, n - 2]][[All, 2]]], {n, 3, 80}]] (* Ivan Neretin, Nov 02 2017 *)
a[n_] := PrimeOmega[Binomial[2*n, n-2]]; Array[a, 100, 2] (* Amiram Eldar, Jun 12 2025 *)

PARI

a(n) = bigomega(binomial(2*n, n-2)); \\ Amiram Eldar, Jun 12 2025

Formula

From Amiram Eldar, Jun 12 2025: (Start)

a(n) = A001222(A002694(n)).

a(n) = A023817(n) - A022559(n+2) + A022559(n-1). (End)

Extensions

Offset corrected to 2 by Ivan Neretin, Nov 02 2017