%I A013959
%S A013959 1,2049,177148,4196353,48828126,362976252,1977326744,8594130945,
%T A013959 31381236757,100048830174,285311670612,743375541244,1792160394038,
%U A013959 4051542498456,8649804864648,17600780175361,34271896307634
%N A013959 sigma_11(n), the sum of the 11-th powers of the divisors of n.
%C A013959 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).
%C A013959 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.
%C A013959 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
%H A013959 T. D. Noe, <a href="b013959.txt">Table of n, a(n) for n=1..1000</a>
%F A013959 G.f. sum(k>=1, k^11*x^k/(1-x^k)). - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Apr 21 2003
%t A013959 lst={};Do[AppendTo[lst,DivisorSigma[11,n]],{n,5!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Mar 11 2009]
%o A013959 (Other) sage: [sigma(n,11)for n in xrange(1,18)] # [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jun 04 2009]
%Y A013959 Sequence in context: A071116 A060949 A017685 this_sequence A036089 A123095 
               A045059
%Y A013959 Adjacent sequences: A013956 A013957 A013958 this_sequence A013960 A013961 
               A013962
%K A013959 nonn,mult
%O A013959 1,2
%A A013959 N. J. A. Sloane (njas(AT)research.att.com).