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

1,2

Comments

a(A071853(n)) = 0.

Links

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

Example

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

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:

Crossrefs

Cf. A067434, A071853.

Sequence in context: A194252 A375982 A205727 * A374263 A338237 A039823

Adjacent sequences: A213606 A213607 A213608 * A213610 A213611 A213612

Keyword

nonn

Author

Michel Lagneau, Jun 16 2012

Status

approved