A023830 Sum of exponents in prime-power factorization of C(4n,n-4).

0, 3, 4, 6, 6, 10, 8, 8, 8, 11, 12, 12, 13, 14, 15, 16, 12, 16, 15, 17, 18, 21, 17, 20, 19, 19, 22, 19, 21, 25, 25, 26, 23, 25, 25, 26, 26, 28, 25, 27, 25, 29, 28, 27, 31, 32, 31, 33, 30, 30, 31, 31, 31, 34, 32, 33, 32, 35, 35, 37, 39, 42, 42, 41, 37, 40, 41, 38, 42, 44, 40, 46, 42, 45, 46, 45, 44

Offset: 4

Author

Clark Kimberling

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 4..10000

Crossrefs

Cf. A001222, A004334, A023826, A023827, A023828, A023829, A023831, A023832, A023833, A023834, A023835, A023836.

Programs

Maple

with(numtheory): A023830:=n->bigomega(binomial(4*n,n-4)): seq(A023830(n), n=4..100); # Wesley Ivan Hurt, Oct 13 2014

Mathematica

Join[{0},Table[Total[Transpose[FactorInteger[Binomial[4n,n-4]]][[2]]],{n,5,80}]] (* Harvey P. Dale, Oct 12 2014 *)
a[n_] := PrimeOmega[Binomial[4*n, n-4]]; Array[a, 100, 4] (* Amiram Eldar, Jun 13 2025 *)

PARI

a(n) = bigomega(binomial(4*n, n-4)); \\ Michel Marcus, Oct 12 2014

Formula

a(n) = Omega( C(4n,n-4) ) = A001222( C(4n,n-4) ), n > 3.

From Amiram Eldar, Jun 13 2025 (Start)

a(n) = A001222(A004334(n)).

a(n) = A023829(n) - A001222(3*n+4) + A001222(n-3). (End)

Extensions

Offset changed by Wesley Ivan Hurt, Oct 13 2014