Search: id:A001160
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%I A001160 M5240 N2279
%S A001160 1,33,244,1057,3126,8052,16808,33825,59293,103158,161052,257908,
%T A001160 371294,554664,762744,1082401,1419858,1956669,2476100,3304182,4101152,
%U A001160 5314716,6436344,8253300,9768751,12252702,14408200,17766056,20511150
%N A001160 sigma_5(n), the sum of the 5th powers of the divisors of n.
%C A001160 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 A001160 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.
%D A001160 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001160 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001160 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math.Series 55, Tenth Printing, 
               1972, p. 827.
%H A001160 T. D. Noe, <a href="b001160.txt">Table of n, a(n) for n = 1..10000</a>
%H A001160 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A001160 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/
               Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</
               a>, National Bureau of Standards Applied Math.Series 55, Tenth Printing, 
               1972, p. 827.
%F A001160 Multiplicative with a(p^e) = (p^(5e+5)-1)/(p^5-1). - David W. Wilson 
               (davidwwilson(AT)comcast.net), Aug 01, 2001.
%F A001160 G.f. sum(k>=1, k^5*x^k/(1-x^k)). - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Apr 21 2003
%t A001160 lst={};Do[AppendTo[lst,DivisorSigma[5,n]],{n,5!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Mar 11 2009]
%o A001160 (Other) sage: [sigma(n,5)for n in xrange(1,30)] # [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jun 04 2009]
%Y A001160 Cf. A000005, A000203, A001157-A001159.
%Y A001160 Sequence in context: A088703 A034679 A017673 this_sequence A061223 A119782 
               A008515
%Y A001160 Adjacent sequences: A001157 A001158 A001159 this_sequence A001161 A001162 
               A001163
%K A001160 nonn,easy,mult
%O A001160 1,2
%A A001160 N. J. A. Sloane (njas(AT)research.att.com).

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