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

0,2

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

Crossrefs

Cf. A001222, A001450, A022559.

Cf. A023816-A023854.

Sequence in context: A230641 A063200 A063224 * A279667 A000061 A153176

Adjacent sequences: A023844 A023845 A023846 * A023848 A023849 A023850

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

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

Status

approved