A152988 Sum of proper divisors minus the number of proper divisors of Catalan number A000108(n).

0, 0, 0, 0, 7, 47, 193, 236, 1579, 4195, 18461, 62143, 275781, 1131909, 7434169, 10522660, 72469339, 268486155, 1442237845, 4284330539, 18146555293, 62021099893, 248289236937, 798007352239, 2832660377605, 11922780595861

Offset: 0

Author

Omar E. Pol, Dec 20 2008, Jan 07 2009

Keywords

• nonn

Examples

			a(5)=47 because A000108(5)=42 has 7 proper divisors: 1,2,3,6,7,14,21 and 1+2+3+6+7+14+21-7 = 47. - _Emeric Deutsch_, Dec 31 2008
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..1667

Crossrefs

Cf. A000005, A000108, A000203, A001065, A032741, A152770.

Programs

Maple

with(numtheory): seq(sigma(binomial(2*n, n)/(n+1))-binomial(2*n, n)/(n+1)-tau(binomial(2*n, n)/(n+1))+1, n = 1 .. 27); # Emeric Deutsch, Dec 31 2008

Mathematica

diff[n_] := DivisorSigma[1, n] - DivisorSigma[0, n] - n + 1; Table[diff[ CatalanNumber[n] ], {n, 0, 25}] (* Amiram Eldar, Dec 01 2019 *)

Formula

a(n) = A001065(A000108(n)) - A032741(A000108(n)) = A152770(A000108(n)).

Extensions

Extended by Emeric Deutsch, Dec 31 2008