A023844 Sum of exponents in prime-power factorization of C(5n,n+2).

2, 4, 4, 7, 7, 8, 9, 10, 10, 11, 12, 14, 15, 13, 14, 17, 15, 16, 16, 20, 19, 18, 18, 22, 19, 22, 24, 24, 26, 24, 24, 25, 24, 24, 24, 28, 26, 26, 28, 31, 27, 31, 27, 31, 34, 30, 31, 31, 33, 33, 35, 39, 36, 38, 38, 40, 37, 41, 40, 45, 44, 38, 37, 40, 40, 40, 38, 40, 44, 41, 44, 47, 43, 45, 45, 47, 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, A023843, A023845, A023846, A023847, A023848, A023849, A023850, A023851.

Programs

Mathematica

Table[PrimeOmega[Binomial[5 n, n + 2]], {n, 77}] (* Ivan Neretin, Nov 08 2017 *)

PARI

a(n) = bigomega(binomial(5*n, n+2)); \\ Michel Marcus, Sep 30 2013

Formula

a(n) = A023843(n) + A001222(4*n-1) - A001222(n+2). - Amiram Eldar, Jun 14 2025