A023843 Sum of exponents in prime-power factorization of C(5n,n+1).

2, 5, 4, 7, 7, 10, 8, 11, 9, 12, 12, 15, 15, 15, 14, 17, 15, 18, 15, 21, 19, 20, 18, 22, 19, 24, 24, 25, 25, 27, 24, 26, 25, 24, 24, 28, 25, 29, 27, 32, 27, 33, 27, 30, 34, 33, 31, 33, 32, 35, 34, 40, 37, 40, 38, 41, 37, 42, 39, 46, 42, 42, 38, 40, 39, 42, 38, 42, 42, 43, 44, 47, 44, 46, 45, 48, 49

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, A023844, A023845, A023846, A023847, A023848, A023849, A023850, A023851.

Programs

Mathematica

Table[PrimeOmega[Binomial[5 n, n + 1]], {n, 77}] (* Ivan Neretin, Nov 08 2017 *)

PARI

a(n) = bigomega(binomial(5*n,n+1)); \\ Amiram Eldar, Jun 14 2025

Formula

a(n) = A023837(n) + A001222(4*n) - A001222(n+1). - Amiram Eldar, Jun 14 2025