A023853 Sum of exponents in prime-power factorization of binomial(6n, 2n).

0, 2, 4, 6, 6, 8, 11, 11, 10, 11, 13, 18, 17, 17, 17, 19, 18, 20, 19, 22, 22, 23, 27, 28, 27, 26, 29, 31, 29, 31, 32, 35, 31, 31, 31, 35, 33, 35, 37, 36, 36, 37, 39, 43, 42, 43, 46, 47, 43, 44, 45, 48, 47, 46, 50, 53, 51, 52, 53, 57, 55, 55, 56, 56, 51, 52, 54, 56, 56, 55, 58, 62, 58, 59, 60, 61, 62

Offset

0,2

Links

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

Formula

From Amiram Eldar, Jun 11 2025: (Start)

a(n) = A001222(3*A259613(n)) for n >= 1.

a(n) = A022559(6*n) - A022559(4*n) - A022559(2*n). (End)

Mathematica

Join[{0}, Table[Total[Transpose[FactorInteger[Binomial[6 n, 2 n]]] [[2]]], {n, 80}]] (* Harvey P. Dale, Jun 28 2011 *)
a[n_] := PrimeOmega[Binomial[6*n, 2*n]]; Array[a, 100, 0] (* Amiram Eldar, Jun 11 2025 *)

Prog

(PARI) a(n) = bigomega(binomial(6*n, 2*n)); \\ Amiram Eldar, Jun 11 2025

Crossrefs

Cf. A001222, A022559, A259613.

Cf. A023852, A023854.

Sequence in context: A347376 A260812 A003972 * A387424 A056526 A049066

Adjacent sequences: A023850 A023851 A023852 * A023854 A023855 A023856

Keyword

nonn

Author

Clark Kimberling

Extensions

a(0)=0 inserted by Amiram Eldar, Jun 11 2025

Status

approved