A023830 - OEIS

%I #21 Nov 02 2017 18:43:49

%S 0,3,4,6,6,10,8,8,8,11,12,12,13,14,15,16,12,16,15,17,18,21,17,20,19,

%T 19,22,19,21,25,25,26,23,25,25,26,26,28,25,27,25,29,28,27,31,32,31,33,

%U 30,30,31,31,31,34,32,33,32,35,35,37,39,42,42,41,37,40,41,38,42,44,40,46,42,45,46,45,44

%N Sum of exponents in prime-power factorization of C(4n,n-4).

%H Ivan Neretin, <a href="/A023830/b023830.txt">Table of n, a(n) for n = 4..10000</a>

%F a(n) = Omega( C(4n,n-4) ) = A001222( C(4n,n-4) ), n > 3.

%p with(numtheory): A023830:=n->bigomega(binomial(4*n,n-4)): seq(A023830(n), n=4..100); # _Wesley Ivan Hurt_, Oct 13 2014

%t Join[{0},Table[Total[Transpose[FactorInteger[Binomial[4n,n-4]]][[2]]],{n,5,80}]] (* _Harvey P. Dale_, Oct 12 2014 *)

%o (PARI) a(n) = bigomega(binomial(4*n, n-4)); \\ _Michel Marcus_, Oct 12 2014

%Y Cf. A001222.

%K nonn

%O 4,2

%A _Clark Kimberling_

%E Offset changed by _Wesley Ivan Hurt_, Oct 13 2014