Search: id:A013954
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%I A013954
%S A013954 1,65,730,4161,15626,47450,117650,266305,532171,1015690,
%T A013954 1771562,3037530,4826810,7647250,11406980,17043521,24137570,
%U A013954 34591115,47045882,65019786,85884500,115151530,148035890
%N A013954 sigma_6(n), the sum of the 6th powers of the divisors of n.
%C A013954 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 A013954 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.
%F A013954 G.f. sum(k>=1, k^6*x^k/(1-x^k)). - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Apr 21 2003
%t A013954 lst={};Do[AppendTo[lst,DivisorSigma[6,n]],{n,5!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Mar 11 2009]
%o A013954 (Other) sage: [sigma(n,6)for n in xrange(1,24)] # [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jun 04 2009]
%Y A013954 Sequence in context: A088677 A034680 A017675 this_sequence A116277 A008516 
               A000540
%Y A013954 Adjacent sequences: A013951 A013952 A013953 this_sequence A013955 A013956 
               A013957
%K A013954 nonn,mult
%O A013954 1,2
%A A013954 N. J. A. Sloane (njas(AT)research.att.com).

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