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Sum of exponents in prime-power factorization of binomial(5n, 2n).
1

%I #23 Jan 19 2019 02:47:47

%S 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,

%T 24,28,26,26,30,29,32,28,30,31,31,32,35,35,36,36,36,37,33,35,38,36,39,

%U 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

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

%H Ivan Neretin, <a href="/A023847/b023847.txt">Table of n, a(n) for n = 0..10000</a> (corrected by Sean A. Irvine, Jan 18 2019)

%F a(n) = A001222(A001450(n)). - _Michel Marcus_, Nov 09 2017

%t Table[PrimeOmega[Binomial[5 n, 2 n]], {n, 77}] (* _Ivan Neretin_, Nov 09 2017 *)

%o (PARI) a(n) = bigomega(binomial(5*n, 2*n)); \\ _Michel Marcus_, Nov 09 2017

%o (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

%o val(n, p) = my(r=0); while(n, r+=n\=p); r \\ _David A. Corneth_, Nov 09 2017

%Y Cf. A001222, A001450, A022559.

%Y Cf. A023816-A023854.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_

%E a(0) = 0 prepended by _David A. Corneth_, Nov 09 2017