A152761 Sum of divisors of Catalan number A000108(n).

1, 1, 3, 6, 24, 96, 336, 672, 3024, 9072, 35280, 120960, 483840, 1874880, 10108800, 20217600, 107827200, 398131200, 1919877120, 6051594240, 24710676480, 86487367680, 339771801600, 1141066967040, 4122564526080, 16784726999040

Offset: 0

Author

Omar E. Pol, Dec 14 2008

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..1667
• Volkan Yildiz, Notes on Divisibility of Catalan Numbers, arXiv:2502.04619 [math.CO], 2025.

Crossrefs

Cf. A000108, A000203, A152762.

Programs

Maple

with(numtheory): seq(sigma(binomial(2*n, n)/(n+1)), n = 0 .. 25); # Emeric Deutsch, Jan 10 2009
A000108 := proc(n) binomial(2*n,n)/(n+1) ; end: A000203 := proc(n) numtheory[sigma](n) ; end: A152761 := proc(n) A000203(A000108(n)) ; end: for n from 0 to 30 do printf("%d,",A152761(n)) ; od: # R. J. Mathar, Jan 08 2009

Mathematica

DivisorSigma[1,CatalanNumber[Range[0,30]]] (* Harvey P. Dale, Apr 17 2015 *)

PARI

a(n) = sigma(binomial(2*n,n)/(n+1)); \\ Michel Marcus, Feb 09 2025

Formula

a(n) = sigma(A000108(n)) = A000203(A000108(n)).

a(n) = A152762(n) + A000108(n). - R. J. Mathar, Jan 08 2009

Extensions

Extended by R. J. Mathar and Emeric Deutsch, Jan 08 2009