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

0,5

Links

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

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A158914 A046872 A167860 * A336789 A201437 A202509

Adjacent sequences: A152985 A152986 A152987 * A152989 A152990 A152991

Keyword

nonn

Author

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

Extensions

Extended by Emeric Deutsch, Dec 31 2008

Status

approved