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

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A001222, A001450, A022559.

Cf. A023816-A023854.

Programs

Mathematica

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

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
val(n, p) = my(r=0); while(n, r+=n\=p); r \\ David A. Corneth, Nov 09 2017

Formula

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

Extensions

a(0) = 0 prepended by David A. Corneth, Nov 09 2017