A152762 Sum of proper divisors of Catalan number A000108(n).
0, 0, 1, 1, 10, 54, 204, 243, 1594, 4210, 18484, 62174, 275828, 1131980, 7434360, 10522755, 72469530, 268486410, 1442238420, 4284331050, 18146556060, 62021100660, 248289237960, 798007353390, 2832660378756, 11922780597588
Offset: 0
Examples
a(4)=10 because the proper divisors of A000108(4)=14 are 1,2 and 7. - _Emeric Deutsch_, Dec 24 2008
Links
- Amiram Eldar, Table of n, a(n) for n = 0..1667
Programs
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Maple
with(numtheory): seq(sigma(binomial(2*n, n)/(n+1))-binomial(2*n, n)/(n+1), n = 0 .. 27); # Emeric Deutsch, Dec 24 2008
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Mathematica
DivisorSigma[1,#]-#&/@CatalanNumber[Range[0,30]] (* Harvey P. Dale, Dec 05 2015 *)
Formula
a(n) = sigma(binomial(2n,n)/(n+1)) - binomial(2n,n)/(n+1), where sigma(m) is the sum of the divisors of m. - Emeric Deutsch, Dec 24 2008
Extensions
Extended by Emeric Deutsch, Dec 24 2008