A121612 Numbers k such that the number of prime divisors of the k-th Catalan number (counted with multiplicity) divides k.

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, 81472, 81528, 81648

Offset: 1

Author

Jonathan Vos Post, Sep 08 2006

Keywords

• nonn

Comments

a(46) > 200000, if it exists. - Amiram Eldar, Oct 10 2024

Examples

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

Crossrefs

Cf. A000108, A001222, A081399.

Programs

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 *)

Formula

{k such that A081399(k)|k} = {k such that A001222(A000108(k))|k}.

Extensions

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

a(43)-a(45) from Amiram Eldar, Oct 10 2024