Search: id:A013972
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%I A013972
%S A013972 1,16777217,282429536482,281474993487873,59604644775390626,
%T A013972 4738381620767930594,191581231380566414402,4722366764344638701569,
%U A013972 79766443077154939399843,1000000059604644792167842,9849732675807611094711842
%N A013972 Sum of 24th powers of divisors of n.
%C A013972 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 A013972 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 A013972 G.f.: sum(k>=1, k^24*x^k/(1-x^k)). - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Apr 21 2003
%t A013972 lst={};Do[AppendTo[lst,DivisorSigma[24,n]],{n,5!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Mar 11 2009]
%o A013972 (Other) sage: [sigma(n,24)for n in xrange(1,12)] # [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jun 04 2009]
%Y A013972 Sequence in context: A017448 A017580 A017711 this_sequence A036102 A143510 
               A043680
%Y A013972 Adjacent sequences: A013969 A013970 A013971 this_sequence A013973 A013974 
               A013975
%K A013972 nonn,mult
%O A013972 1,2
%A A013972 N. J. A. Sloane (njas(AT)research.att.com).

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