A023838 Sum of exponents in prime-power factorization of C(5n,n-1).

0, 2, 3, 5, 5, 7, 8, 9, 8, 10, 10, 12, 14, 13, 15, 14, 14, 16, 14, 17, 17, 18, 18, 21, 18, 22, 24, 23, 23, 24, 24, 24, 23, 23, 24, 25, 24, 26, 28, 29, 25, 30, 27, 29, 33, 30, 30, 32, 32, 33, 33, 37, 37, 38, 38, 37, 36, 40, 39, 44, 39, 41, 40, 39, 37, 39, 38, 39, 42, 41, 44, 44, 43, 43, 44, 46, 48, 49

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222, A004343, A023837, A023839, A023840, A023841, A023842, A023843, A023844, A023845, A023846, A023847, A023848, A023849, A023850, A023851.

Programs

Mathematica

Join[{0},Table[Total[Transpose[FactorInteger[Binomial[5 n,n-1]]] [[2]]],{n,2,80}]] (* Harvey P. Dale, Dec 31 2012 *)
a[n_] := PrimeOmega[Binomial[5*n, n-1]]; Array[a, 100] (* Amiram Eldar, Jun 14 2025 *)

PARI

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

Formula

From Amiram Eldar, Jun 14 2025: (Start)

a(n) = A001222(A004343(n)).

a(n) = A023837(n) - A001222(4*n+1) + A001222(n). (End)