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A152988 Sum of proper divisors minus the number of proper divisors of Catalan number A000108(n). 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 24 05:05 EDT 2021. Contains 346273 sequences. (Running on oeis4.)