

A013959


a(n) = sigma_11(n), the sum of the 11th powers of the divisors of n.


18



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

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^k1).
Sum_{dn} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665A017712 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), A001157A001160 (k=2,3,4,5), A013954A013972 for k = 6,7,...,24.  Ahmed Fares (ahmedfares(AT)mydeja.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


LINKS

T. D. Noe, Table of n, a(n) for n=1..1000
Index entries for sequences related to sigma(n)


FORMULA

G.f.: sum(k>=1, k^11*x^k/(1x^k)).  Benoit Cloitre, Apr 21 2003
Dirichlet g.f.: zeta(s11)*zeta(s).  Ilya Gutkovskiy, Sep 10 2016


MATHEMATICA

Table[DivisorSigma[11, n], {n, 30}] (* Vincenzo Librandi, Sep 10 2016 *)


PROG

(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/(1q^n))) \\ Altug Alkan, Sep 10 2016
(MAGMA) [DivisorSigma(11, n): n in [1..20]]; // Vincenzo Librandi, Sep 10 2016


CROSSREFS

Cf. A000594, A027860, A046694.
Sequence in context: A230189 A321808 A017685 * A036089 A123095 A174752
Adjacent sequences: A013956 A013957 A013958 * A013960 A013961 A013962


KEYWORD

nonn,mult,easy,changed


AUTHOR

N. J. A. Sloane


STATUS

approved



