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Search: id:A013961
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| A013961 |
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sigma_13(n), the sum of the 13th powers of the divisors of n. |
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+0
3
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| 1, 8193, 1594324, 67117057, 1220703126, 13062296532, 96889010408, 549822930945, 2541867422653, 10001220711318, 34522712143932, 107006334784468, 302875106592254, 793811662272744, 1946196290656824
(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^13*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[13, n]], {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 11 2009]
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PROGRAM
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(Other) sage: [sigma(n, 13)for n in xrange(1, 16)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 04 2009]
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CROSSREFS
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Sequence in context: A138031 A035908 A017689 this_sequence A036091 A045060 A031844
Adjacent sequences: A013958 A013959 A013960 this_sequence A013962 A013963 A013964
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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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