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Smallest number k such that the number of distinct prime divisors of binomial(2k,k) equals n, otherwise 0.
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%I #6 Jun 16 2012 06:36:02

%S 1,2,4,6,8,11,15,16,18,20,0,28,29,33,38,42,45,48,53,54,60,64,66,67,75,

%T 77,80,86,91,92,100,102,104,109,111,110,127,0,128,133,140,144,151,154,

%U 153,160,165,170,171,178,0,189,190,192,198,202,209,210,220,225

%N Smallest number k such that the number of distinct prime divisors of binomial(2k,k) equals n, otherwise 0.

%C a(A071853(n)) = 0.

%H Olivier GĂ©rard, <a href="/A213609/b213609.txt">Table of n, a(n) for n = 1..1000</a>

%e a(3) = 4 because binomial(2*4,4) = 70 with 3 distinct prime divisors {2, 5, 7}.

%p with(numtheory): for n from 1 to 100 do:ii:=0: for k from 1 to 500 while(ii=0) do:x:=binomial(2*k,k):y:=factorset(x): n1:=nops(y):if n1=n then ii:=1:printf(`%d, `,k):else fi:od:if ii=0 then printf(`%d, `,0):else fi:od:

%Y Cf. A067434, A071853.

%K nonn

%O 1,2

%A _Michel Lagneau_, Jun 16 2012