%I A013971
%S A013971 1,8388609,94143178828,70368752566273,11920928955078126,
%T A013971 789730317205170252,27368747340080916344,590295880727458217985,
%U A013971 8862938119746644274757,100000011920928963466734,895430243255237372246532
%N A013971 Sum of 23rd powers of divisors of n.
%C A013971 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 A013971 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 A013971 G.f. sum(k>=1, k^23*x^k/(1-x^k)). - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Apr 21 2003
%t A013971 lst={};Do[AppendTo[lst,DivisorSigma[23,n]],{n,5!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Mar 11 2009]
%o A013971 (Other) sage: [sigma(n,23)for n in xrange(1,12)] # [From Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jun 04 2009]
%Y A013971 Sequence in context: A017710 A010811 A017709 this_sequence A036101 A160673 
               A049362
%Y A013971 Adjacent sequences: A013968 A013969 A013970 this_sequence A013972 A013973 
               A013974
%K A013971 nonn,mult
%O A013971 1,2
%A A013971 N. J. A. Sloane (njas(AT)research.att.com).