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A121612 Numbers n such that bigomega of n-th Catalan number divides n. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A073465 A174816 A161494 * A061193 A180941 A190896

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

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Last modified December 10 13:37 EST 2016. Contains 279004 sequences.