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A013959
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a(n) = sigma_11(n), the sum of the 11th powers of the divisors of n.
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18
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1, 2049, 177148, 4196353, 48828126, 362976252, 1977326744, 8594130945, 31381236757, 100048830174, 285311670612, 743375541244, 1792160394038, 4051542498456, 8649804864648, 17600780175361, 34271896307634, 64300154115093, 116490258898220, 204900053024478
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OFFSET
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1,2
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COMMENTS
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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. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001
Related to congruence properties of the Ramanujan tau function since A000594(n) == a(n) (mod 691) = A046694(n). - Benoit Cloitre, Aug 28 2002
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Index entries for sequences related to sigma(n)
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FORMULA
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G.f.: sum(k>=1, k^11*x^k/(1-x^k)). - Benoit Cloitre, Apr 21 2003
Dirichlet g.f.: zeta(s-11)*zeta(s). - Ilya Gutkovskiy, Sep 10 2016
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MATHEMATICA
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Table[DivisorSigma[11, n], {n, 30}] (* Vincenzo Librandi, Sep 10 2016 *)
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PROG
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(Sage) [sigma(n, 11)for n in range(1, 18)] # Zerinvary Lajos, Jun 04 2009
(PARI) a(n)=sigma(n, 11) \\ Charles R Greathouse IV, Apr 28, 2011
(PARI) N=99; q='q+O('q^N); Vec(sum(n=1, N, n^11*q^n/(1-q^n))) \\ Altug Alkan, Sep 10 2016
(MAGMA) [DivisorSigma(11, n): n in [1..20]]; // Vincenzo Librandi, Sep 10 2016
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CROSSREFS
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Cf. A000594, A027860, A046694.
Sequence in context: A230189 A321808 A017685 * A036089 A123095 A174752
Adjacent sequences: A013956 A013957 A013958 * A013960 A013961 A013962
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KEYWORD
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nonn,mult,easy,changed
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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