A023835 Sum of exponents in prime-power factorization of C(4n,2n-1).

2, 4, 6, 7, 7, 9, 11, 12, 13, 13, 13, 15, 14, 16, 17, 18, 16, 18, 18, 20, 22, 22, 23, 25, 24, 24, 25, 24, 24, 28, 27, 29, 27, 30, 30, 32, 31, 31, 34, 32, 31, 33, 34, 37, 36, 35, 36, 40, 37, 37, 38, 39, 39, 42, 41, 42, 42, 42, 42, 43, 44, 46, 47, 48, 45, 46, 44, 45, 48, 49, 47, 50, 47, 49, 53, 52, 51

Offset

1,1

Links

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

Formula

a(n) = A023832(n) - A001222(2*n+1) + A001222(2*n) = A023832(n) - A076191(2*n). - Amiram Eldar, Jun 13 2025

Mathematica

Table[PrimeOmega[Binomial[4 n, 2 n - 1]], {n, 78}] (* Ivan Neretin, Nov 08 2017 *)

Prog

(PARI) a(n) = bigomega(binomial(4*n, 2*n-1)); \\ Amiram Eldar, Jun 13 2025

Crossrefs

Cf. A001222, A023826, A023827, A023828, A023829, A023830, A023831, A023832, A023834, A023836, A076191.

Sequence in context: A087777 A030118 A331379 * A272633 A240817 A381226

Adjacent sequences: A023832 A023833 A023834 * A023836 A023837 A023838

Keyword

nonn

Author

Clark Kimberling

Extensions

a(74)-a(77) corrected by Ivan Neretin, Nov 08 2017

Status

approved