A023823 Sum of exponents in prime-power factorization of C(3n,n+1).

1, 3, 4, 6, 4, 8, 7, 8, 8, 10, 10, 14, 11, 12, 11, 14, 11, 14, 14, 15, 14, 20, 16, 20, 17, 17, 20, 20, 17, 22, 19, 22, 19, 21, 20, 23, 21, 23, 22, 26, 20, 26, 27, 28, 29, 30, 27, 31, 28, 28, 28, 32, 26, 34, 31, 32, 32, 33, 33, 36, 33, 35, 32, 36, 30, 34, 33, 33, 32, 38, 33, 38, 34, 35, 39, 39, 36, 39

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A001222, A023819, A023820, A023821, A023822, A023824, A023825.

Programs

Mathematica

Table[Total[FactorInteger[Binomial[3 n, n + 1]][[All, 2]]], {n, 78}] (* Ivan Neretin, Nov 02 2017 *)
a[n_] := PrimeOmega[Binomial[3*n, n+1]]; Array[a, 100] (* Amiram Eldar, Jun 12 2025 *)

PARI

a(n) = bigomega(binomial(3*n, n+1)); \\ Amiram Eldar, Jun 12 2025

Formula

a(n) = A023819(n) + A001222(2*n) - A001222(n+1). - Amiram Eldar, Jun 12 2025

Extensions

a(53) corrected by Ivan Neretin, Nov 02 2017