A023837 Sum of exponents in prime-power factorization of C(5n,n).

0, 1, 3, 3, 4, 6, 7, 8, 8, 7, 9, 12, 11, 14, 13, 14, 12, 15, 14, 15, 18, 17, 17, 19, 18, 17, 23, 22, 21, 25, 23, 26, 21, 23, 22, 24, 23, 24, 27, 27, 27, 27, 29, 27, 28, 31, 30, 33, 28, 31, 32, 33, 36, 38, 36, 38, 37, 35, 39, 40, 41, 41, 41, 39, 34, 38, 38, 38, 39, 41, 39, 46, 41, 43, 45, 43, 45, 48, 47

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001222, A001449, A023838, A023839, A023840, A023841, A023842, A023843, A023844, A023845, A023846, A023847, A023848, A023849, A023850, A023851.

Programs

Maple

with(numtheory):a:=proc(n) if n=0 then 0 else bigomega(binomial(5*n,n)) fi end: seq(a(n), n=0..78); # Zerinvary Lajos, Apr 11 2008

Mathematica

Table[PrimeOmega[Binomial[5 n, n]], {n, 0, 78}] (* Ivan Neretin, Nov 08 2017 *)

PARI

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

Formula

a(n) = A001222(A001449(n)). - Amiram Eldar, Jun 14 2025

Extensions

Offset changed to 0 and a(0) prepended by Amiram Eldar, Jun 14 2025