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%I #2 Mar 30 2012 17:22:54
%S 4,4,6,24,60,144,360,852,1968,4488,10068,22272,48780,105948,228588,
%T 490404,1046976,2225964,4715400,9956976,20965212,44031360,92262348,
%U 192920784,402629256,838827576,1744784388,3623814864,7516104564
%N Least number k such that sigma_n(k) > sigma_n(k+1), where sigma_n(k) = sum of the n-th powers of the divisors of k.
%C It appears that the inequality a(n+1) > (2+2/n)*a(n) is true for n > 4.
%F For n>0, a(n) = A098475(n) - 1.
%e The values of the sigma_3 function (A001158) are increasing up to 25. Hence a(3)=24.
%t Join[{4,4}, Table[k=Floor[NSolve[Zeta[n](x-1)^n==x^n, x, WorkingPrecision->100][[ -1,1,2]]]; While[DivisorSigma[n,k]<DivisorSigma[n,k+1], k++ ]; k, {n,2,30}]]
%K nonn
%O 0,1
%A _T. D. Noe_, Mar 23 2009
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