A023851 Sum of exponents in prime-power factorization of binomial(5n, 2n+2).

1, 4, 5, 6, 8, 9, 10, 12, 12, 13, 15, 15, 16, 16, 17, 19, 18, 20, 18, 23, 25, 21, 22, 24, 24, 28, 29, 27, 29, 31, 28, 31, 32, 30, 32, 35, 34, 34, 36, 37, 35, 40, 36, 35, 39, 36, 37, 40, 38, 41, 43, 46, 46, 46, 45, 48, 46, 49, 47, 51, 52, 50, 48, 49, 51, 52, 49, 52, 55, 53, 54, 58, 55, 57, 60, 58, 62

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A001222, A023837, A023839, A023840, A023841, A023842, A023843, A023844, A023845, A023846, A023847, A023848, A023849, A023851.

Programs

Mathematica

Table[PrimeOmega[Binomial[5 n, 2 n + 2]], {n, 77}] (* Ivan Neretin, Nov 09 2017 *)

PARI

a(n) = bigomega(binomial(5*n,2*n+2)); \\ Amiram Eldar, Jun 14 2025

Formula

a(n) = A023850(n) + A001222(3*n-1) - A001222(2*n+2). - Amiram Eldar, Jun 14 2025

Extensions

Missing terms a(31), a(32) fixed by Ivan Neretin, Nov 09 2017