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%I #9 Nov 21 2013 12:48:59
%S 15,20,42,77,88,104,126,140,153,156,170,187,190,204,209,210,220,228,
%T 231,238,240,266,299,308,312,322,368,420,429,435,440,442,450,460,464,
%U 468,476,483,493,496,510,527,551,558,561,580,589,600,609,620,624,651,665
%N Numbers n such that the n-th Catalan number C(2n,n)/(n+1) is divisible by 3n.
%C Equivalently, numbers n such that the n-th central binomial coefficient C(2n,n) is divisible by 3n(n+1). - _Joel B. Lewis_, Jan 07 2008
%H Harvey P. Dale, <a href="/A120625/b120625.txt">Table of n, a(n) for n = 1..1000</a>
%t fQ[n_] := fQ[n_] := IntegerQ[ Binomial[2n, n]/(3n(n + 1))]; Select[ Range@681, fQ@# &]
%t With[{nn=700},Transpose[Select[Thread[{CatalanNumber[Range[nn]],Range[ nn]}],Divisible[#[[1]],3#[[2]]]&]][[2]]] (* _Harvey P. Dale_, Apr 30 2012 *)
%Y Subset of A104847, Cf. A120623.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Jun 19 2006
%E Definition corrected by _Joel B. Lewis_, Apr 30 2009
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