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%I #9 Mar 14 2015 18:02:30
%S 2,3,4,8,10,12,16,20,22,117,408,432,444,492,504,508,1555,1560,1605,
%T 1675,1790,5832,5940,5976,6048,6078,6102,6108,6132,6138,21175,21266,
%U 21280,21301,21434,21462,21469,21616,21623,21749,21770,21784
%N Numbers n such that bigomega of n-th Catalan number divides n.
%C The number of prime divisors of n-th Catalan number (counted with multiplicity) divides n.
%F {n such that A081399(n)|n} = {n such that A001222[A000108(n)]|n}.
%e a(1) = 2 because bigomega(Catalan(2)) = bigomega(2) = 1 and 1 | 2.
%t 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 *)
%Y Cf. A000108, A001222, A081399.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Sep 08 2006
%E Corrected and extended (a(10)-a(42)) by _Robert G. Wilson v_, Sep 11 2006
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