Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Sep 30 2013 09:39:52
%S 1,1,2,3,1,2,5,3,5,6,4,6,6,3,4,6,5,4,6,5,8,10,7,9,9,7,9,8,7,10,12,10,
%T 9,13,11,13,16,12,13,14,9,11,12,12,13,12,12,13,15,11,13,16,13,15,17,
%U 16,19,19,16,15,17,18,15,18,17,19,19,13,17,19,17,18,18,15,19,21,18,17,20,19,19,22,19,22
%N Sum of exponents of primes in C(4n,2n)/C(2n,n).
%H Charles R Greathouse IV, <a href="/A023986/b023986.txt">Table of n, a(n) for n = 1..10000</a>
%o (PARI) a(n) = my(v = binomial(4*n, 2*n)/binomial(2*n, n)); bigomega(numerator(v)) - bigomega(denominator(v)); \\ _Michel Marcus_, Sep 30 2013
%o (PARI) vp(n,p)=my(s);while(n\=p,s+=n);s
%o a(n)=my(s);forprime(p=2,4*n,s+=vp(4*n,p)-3*vp(2*n,p)+2*vp(n,p)); s \\ _Charles R Greathouse IV_, Sep 30 2013
%K nonn
%O 1,3
%A _Clark Kimberling_