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%I #11 Oct 31 2015 05:30:19
%S 0,1,1,1,2,2,2,3,2,1,3,2,3,3,3,3,4,5,5,6,5,4,4,4,4,4,3,5,7,5,5,6,7,6,
%T 6,5,5,6,5,5,6,6,7,7,7,7,8,9,8,8,7,6,8,8,6,6,5,6,7,8,9,9,9,9,9,9,11,
%U 10,9,8,9,10,11,11,11,10,11,11,11,12,12,11
%N Number of distinct prime factors <= n of binomial(2*n,n).
%H T. D. Noe, <a href="/A193990/b193990.txt">Table of n, a(n) for n = 1..10000</a>
%p a := n -> nops(numtheory:-factorset(binomial(2*n,n)) minus select(isprime, {$n+1..2*n})): seq(a(n), n=1..82); # _Peter Luschny_, Oct 31 2015
%t Table[Length[Select[Transpose[FactorInteger[Binomial[2 n, n]]][[1]], # <= n &]], {n, 100}]
%o (PARI) valp(n, p)=my(s); while(n\=p, s+=n); s
%o a(n)=my(s); forprime(p=2, n, if(valp(2*n, p)>2*valp(n, p), s++)); s \\ _Charles R Greathouse IV_, May 25 2013
%Y Cf. A067434 (number of prime factors in binomial(2*n,n)), A108954.
%K nonn
%O 1,5
%A _T. D. Noe_, Aug 17 2011
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