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 A013957 sigma_9(n), the sum of the 9th powers of the divisors of n. 21
 1, 513, 19684, 262657, 1953126, 10097892, 40353608, 134480385, 387440173, 1001953638, 2357947692, 5170140388, 10604499374, 20701400904, 38445332184, 68853957121, 118587876498, 198756808749, 322687697780, 513002215782 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_p ((p^((e(p)+1)*k))-1)/(p^k-1). Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 FORMULA G.f. Sum(k>=1, k^9*x^k/(1-x^k)). - Benoit Cloitre, Apr 21 2003 L.g.f.: -log(Product_{k>=1} (1 - x^k)^(k^8)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 06 2017 MATHEMATICA Table[DivisorSigma[9, n], {n, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *) PROG (PARI) a(n)=if(n<1, 0, sigma(n, 9)) (Sage) [sigma(n, 9)for n in range(1, 21)] # Zerinvary Lajos, Jun 04 2009 (MAGMA) [DivisorSigma(9, n): n in [1..20]]; // Bruno Berselli, Apr 10 2013 CROSSREFS Sequence in context: A223651 A321565 A017681 * A294304 A036087 A007487 Adjacent sequences:  A013954 A013955 A013956 * A013958 A013959 A013960 KEYWORD nonn,mult,easy AUTHOR STATUS approved

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Last modified October 25 15:37 EDT 2020. Contains 338012 sequences. (Running on oeis4.)