A023845 Sum of exponents in prime-power factorization of binomial(5n, n+3).

1, 5, 4, 8, 7, 8, 9, 12, 9, 12, 13, 14, 14, 16, 13, 18, 15, 17, 16, 22, 17, 18, 20, 21, 19, 24, 23, 26, 24, 24, 24, 27, 23, 25, 25, 28, 24, 29, 28, 32, 29, 30, 28, 33, 31, 31, 31, 32, 32, 36, 33, 39, 36, 38, 38, 42, 35, 43, 42, 45, 41, 39, 38, 41, 40, 40, 38, 44, 41, 42, 45, 47, 43, 47, 44, 48, 48

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

Programs

Mathematica

Table[Total[Transpose[FactorInteger[Binomial[5n,n+3]]][[2]]],{n,80}] (* Harvey P. Dale, Aug 12 2012 *)
a[n_] := PrimeOmega[Binomial[5*n, n+3]]; Array[a, 100] (* Amiram Eldar, Jun 14 2025 *)

PARI

a(n) = bigomega(binomial(5*n,n+3)); \\ Amiram Eldar, Jun 14 2025

Formula

a(n) = A023844(n) + A001222(4*n-2) - A001222(n+3). - Amiram Eldar, Jun 14 2025