A023986 - 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_