A213609 Smallest number k such that the number of distinct prime divisors of binomial(2k,k) equals n, otherwise 0.

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, 77, 80, 86, 91, 92, 100, 102, 104, 109, 111, 110, 127, 0, 128, 133, 140, 144, 151, 154, 153, 160, 165, 170, 171, 178, 0, 189, 190, 192, 198, 202, 209, 210, 220, 225

Offset: 1

Author

Michel Lagneau, Jun 16 2012

Keywords

• nonn

Comments

a(A071853(n)) = 0.

Examples

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

Links

• Olivier Gérard, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A067434, A071853.

Programs

Maple

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: