A120625 Numbers n such that the n-th Catalan number C(2n,n)/(n+1) is divisible by 3n.

15, 20, 42, 77, 88, 104, 126, 140, 153, 156, 170, 187, 190, 204, 209, 210, 220, 228, 231, 238, 240, 266, 299, 308, 312, 322, 368, 420, 429, 435, 440, 442, 450, 460, 464, 468, 476, 483, 493, 496, 510, 527, 551, 558, 561, 580, 589, 600, 609, 620, 624, 651, 665

Offset: 1

Author

Robert G. Wilson v, Jun 19 2006

Keywords

• nonn

Comments

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Subset of A104847, Cf. A120623.

Programs

Mathematica

fQ[n_] := fQ[n_] := IntegerQ[ Binomial[2n, n]/(3n(n + 1))]; Select[ Range@681, fQ@# &]
With[{nn=700},Transpose[Select[Thread[{CatalanNumber[Range[nn]],Range[ nn]}],Divisible[#[[1]],3#[[2]]]&]][[2]]] (* Harvey P. Dale, Apr 30 2012 *)

Extensions

Definition corrected by Joel B. Lewis, Apr 30 2009