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
Keywords
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
Programs
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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:
Comments