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Search: id:A013959
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| A013959 |
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sigma_11(n), the sum of the 11-th powers of the divisors of n. |
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+0
6
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| 1, 2049, 177148, 4196353, 48828126, 362976252, 1977326744, 8594130945, 31381236757, 100048830174, 285311670612, 743375541244, 1792160394038, 4051542498456, 8649804864648, 17600780175361, 34271896307634
(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.
Related to congruence properties of the Ramanujan tau function T since T(n)==a(n) (mod 691) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 28 2002
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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G.f. sum(k>=1, k^11*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[11, 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, 11)for n in xrange(1, 18)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 04 2009]
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CROSSREFS
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Sequence in context: A071116 A060949 A017685 this_sequence A036089 A123095 A045059
Adjacent sequences: A013956 A013957 A013958 this_sequence A013960 A013961 A013962
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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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