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 #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 Gérard, <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