A023817 Sum of exponents in prime-power factorization of C(2n,n-1).

0, 2, 2, 4, 4, 6, 4, 7, 6, 7, 6, 9, 8, 11, 9, 12, 9, 13, 10, 13, 12, 13, 12, 15, 14, 14, 14, 16, 14, 17, 12, 18, 16, 16, 15, 18, 15, 18, 17, 20, 19, 22, 20, 22, 22, 23, 20, 25, 21, 24, 22, 24, 22, 25, 21, 24, 22, 24, 23, 28, 26, 27, 26, 29, 25, 27, 25, 30, 28, 30, 26, 32, 29, 31, 31, 31, 31, 34, 29, 32

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A001791, A023816, A023818, A076191.

Programs

Mathematica

Join[{0},Total[FactorInteger[#][[All,2]]]&/@Table[Binomial[2n,n-1], {n,2,80}]] (* Harvey P. Dale, Sep 14 2016 *)
Table[PrimeOmega[Binomial[2 n, n + 1]], {n, 1, 200}] (* Clark Kimberling, May 04 2025 *)

PARI

a(n) = bigomega(binomial(2*n, n-1)); \\ Amiram Eldar, Jun 11 2025

Formula

From Amiram Eldar, Jun 11 2025: (Start)

a(n) = A001222(A001791(n)).

a(n) = A023816(n) - A076191(n). (End)