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%I #27 Oct 18 2017 02:49:18
%S 1,2,2,3,3,4,4,5,5,5,6,6,6,6,7,8,8,9,9,10,10,10,9,10,10,10,10,12,13,
%T 12,12,13,14,14,14,14,14,15,14,15,15,16,16,16,17,17,17,18,18,18,18,18,
%U 19,20,19,19,19,20,20,21,21,21,21,22,22,23,24,23,23,23,23,24,24,24,25,25
%N Number of distinct prime factors in binomial(2*n,n).
%C a(n) = A001221(A000984(n)) = length of n-th row in A226078. - _Reinhard Zumkeller_, May 25 2013
%H T. D. Noe, <a href="/A067434/b067434.txt">Table of n, a(n) for n=1..10000</a>
%F a(n) ~ kn/log n, with k = log 4. - _Charles R Greathouse IV_, May 25 2013
%p a := n -> nops(numtheory:-factorset(binomial(2*n,n))):
%p seq(a(n), n=1..76); # _Peter Luschny_, Oct 31 2015
%t Table[Length[FactorInteger[Binomial[2 n, n]]], {n, 100}] (* _T. D. Noe_, Aug 17 2011 *)
%o (Haskell)
%o a067434 = a001221 . a000984 -- _Reinhard Zumkeller_, May 25 2013
%o (PARI) a(n)=omega(binomial(2*n,n)) \\ _Charles R Greathouse IV_, May 25 2013
%o (PARI) valp(n,p)=my(s);while(n\=p,s+=n);s
%o a(n)=my(s);forprime(p=2,2*n,if(valp(2*n,p)>2*valp(n,p),s++)); s \\ _Charles R Greathouse IV_, May 25 2013
%Y Cf. A193990, A193991 (number of prime factors <= n and > n).
%K easy,nonn
%O 1,2
%A _Benoit Cloitre_, Feb 23 2002
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