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Search: id:A013957
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| A013957 |
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sigma_9(n), the sum of the 9th powers of the divisors of n. |
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+0
6
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| 1, 513, 19684, 262657, 1953126, 10097892, 40353608, 134480385, 387440173, 1001953638, 2357947692, 5170140388, 10604499374, 20701400904, 38445332184, 68853957121, 118587876498, 198756808749, 322687697780, 513002215782
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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. - comment from Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001.
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FORMULA
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G.f. sum(k>=1, k^9*x^k/(1-x^k)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 21 2003
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MATHEMATICA
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lst={}; Do[AppendTo[lst, DivisorSigma[9, n]], {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 11 2009]
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PROGRAM
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(PARI) a(n)=if(n<1, 0, sigma(n, 9))
(Other) sage: [sigma(n, 9)for n in xrange(1, 21)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 04 2009]
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CROSSREFS
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Sequence in context: A076338 A111344 A017681 this_sequence A036087 A007487 A023878
Adjacent sequences: A013954 A013955 A013956 this_sequence A013958 A013959 A013960
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KEYWORD
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nonn,mult
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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