A023842 Sum of exponents in prime-power factorization of C(5n,n-5).

0, 3, 3, 6, 6, 8, 8, 11, 10, 12, 9, 13, 13, 15, 11, 17, 16, 16, 15, 18, 16, 22, 22, 23, 22, 23, 20, 22, 22, 24, 22, 27, 22, 25, 25, 26, 24, 29, 24, 29, 30, 28, 27, 31, 31, 33, 32, 39, 35, 37, 34, 39, 36, 41, 38, 39, 37, 37, 34, 37, 39, 43, 38, 41, 40, 40, 39, 44, 40, 42, 42, 46, 47, 49, 46, 46, 47

Offset: 5

Author

Clark Kimberling

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 5..10000

Crossrefs

Cf. A001222, A004347, A023837, A023838, A023839, A023840, A023841, A023843, A023844, A023845, A023846, A023847, A023848, A023849, A023850, A023851.

Programs

Mathematica

Table[PrimeOmega[Binomial[5 n, n - 5]], {n, 5, 81}] (* Ivan Neretin, Nov 08 2017 *)

PARI

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

Formula

From Amiram Eldar, Jun 14 2025: (Start)

a(n) = A001222(A004347(n)).

a(n) = A023841(n) - A001222(4*n+5) + A001222(n-4). (End)

Extensions

Offset corrected to 5 by Ivan Neretin, Nov 08 2017