A121612 Numbers n such that bigomega of n-th Catalan number divides n.

2, 3, 4, 8, 10, 12, 16, 20, 22, 117, 408, 432, 444, 492, 504, 508, 1555, 1560, 1605, 1675, 1790, 5832, 5940, 5976, 6048, 6078, 6102, 6108, 6132, 6138, 21175, 21266, 21280, 21301, 21434, 21462, 21469, 21616, 21623, 21749, 21770, 21784

Offset

1,1

Comments

The number of prime divisors of n-th Catalan number (counted with multiplicity) divides n.

Links

Table of n, a(n) for n=1..42.

Formula

{n such that A081399(n)|n} = {n such that A001222[A000108(n)]|n}.

Example

a(1) = 2 because bigomega(Catalan(2)) = bigomega(2) = 1 and 1 | 2.

Mathematica

fQ[n_] := Mod[n, Plus @@ (Last@# & /@ FactorInteger[ Binomial[2n, n]/(n + 1)])] == 0; s = {}; Do[ If[fQ@n, Print@n; AppendTo[s, n]], {n, 2, 35500}] (* Robert G. Wilson v, Sep 11 2006 *)

Crossrefs

Cf. A000108, A001222, A081399.

Sequence in context: A161494 A356641 A296161 * A061193 A346971 A180941

Adjacent sequences: A121609 A121610 A121611 * A121613 A121614 A121615

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 08 2006

Extensions

Corrected and extended (a(10)-a(42)) by Robert G. Wilson v, Sep 11 2006

Status

approved