A120624 Numbers n such that the n-th Catalan number C(2n,n)/(n+1) is divisible by 2n.

6, 28, 42, 45, 66, 77, 91, 110, 126, 140, 153, 156, 170, 187, 190, 204, 209, 210, 220, 228, 231, 238, 266, 276, 299, 308, 312, 315, 322, 325, 330, 345, 378, 414, 420, 429, 435, 440, 442, 450, 459, 460, 468, 476, 483, 493, 496, 510, 527, 551, 558, 561, 570

Offset: 1

Author

Robert G. Wilson v, Jun 19 2006

Keywords

• nonn

Comments

Equivalently, numbers such that the n-th central binomial coefficient C(2n, n) is divisible by 2n(n + 1). - Joel B. Lewis, Jan 07 2008

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Subset of A014847.

Cf. A120622.

Programs

Mathematica

fQ[n_] := fQ[n_] := IntegerQ[ Binomial[2n, n]/(2n(n + 1))]; Select[ Range@8719, fQ@# &]
Select[Range[600],Divisible[CatalanNumber[#],2#]&] (* Harvey P. Dale, Aug 30 2016 *)

Python

from _future_ import division
A120624_list, b = [], 1
for n in range(1,10**5):
    if not b % (2*n):
        A120624_list.append(n)
    b = b*(4*n+2)//(n+2) # Chai Wah Wu, Mar 25 2016

Extensions

Definition corrected by Joel B. Lewis, Apr 30 2009