A023827 Sum of exponents in prime-power factorization of C(4n,n-1).

0, 3, 3, 6, 4, 7, 8, 10, 9, 11, 8, 11, 10, 15, 14, 16, 13, 16, 14, 18, 15, 17, 17, 21, 20, 21, 19, 20, 18, 22, 21, 26, 21, 26, 24, 27, 23, 26, 28, 28, 28, 30, 26, 30, 27, 29, 29, 33, 30, 33, 30, 33, 30, 33, 31, 33, 31, 33, 32, 36, 35, 39, 39, 42, 37, 40, 38, 41, 40, 42, 40, 44, 41, 45, 44, 46, 44, 46

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A001222, A004331, A022559, A023826.

Programs

Mathematica

Join[{0},Table[Total[Transpose[FactorInteger[Binomial[4n,n-1]]] [[2]]],{n,2,80}]] (* Harvey P. Dale, Jun 13 2013 *)
a[n_] := PrimeOmega[Binomial[4*n, n-1]]; Array[a, 100] (* Amiram Eldar, Jun 11 2025 *)

PARI

a(n) = bigomega(binomial(4*n, n-1)); \\ Amiram Eldar, Jun 11 2025

Formula

From Amiram Eldar, Jun 11 2025: (Start)

a(n) = A001222(A004331(n)). - Amiram Eldar, Jun 11 2025

a(n) = A022559(4*n) - A022559(3*n+1) - A022559(n-1).

a(n) = A023826(n) - A001222(3*n+1) + A001222(n). (End)