A023847 - OEIS

A023847

Sum of exponents in prime-power factorization of binomial(5n, 2n).

0, 2, 4, 4, 6, 8, 8, 11, 11, 11, 13, 13, 13, 18, 16, 17, 17, 19, 18, 18, 22, 24, 21, 23, 23, 24, 28, 26, 26, 30, 29, 32, 28, 30, 31, 31, 32, 35, 35, 36, 36, 36, 37, 33, 35, 38, 36, 39, 36, 40, 40, 41, 45, 48, 43, 46, 46, 45, 50, 47, 49, 52, 52, 49, 46, 51, 51, 50, 50, 55, 51, 57, 54, 57, 57, 55, 59, 62

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OFFSET

0,2

LINKS

Ivan Neretin, Table of n, a(n) for n = 0..10000 (corrected by Sean A. Irvine, Jan 18 2019)

FORMULA

a(n) = A001222(A001450(n)). - Michel Marcus, Nov 09 2017

MATHEMATICA

Table[PrimeOmega[Binomial[5 n, 2 n]], {n, 77}] (* Ivan Neretin, Nov 09 2017 *)

PROG

(PARI) a(n) = bigomega(binomial(5*n, 2*n)); \\ Michel Marcus, Nov 09 2017

(PARI) a(n) = my(res = 0); forprime(p = 2, 5*n, res += (val(5*n, p) - val(2*n, p) - val(3*n, p))); res