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A158661
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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.
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0
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4, 4, 6, 24, 60, 144, 360, 852, 1968, 4488, 10068, 22272, 48780, 105948, 228588, 490404, 1046976, 2225964, 4715400, 9956976, 20965212, 44031360, 92262348, 192920784, 402629256, 838827576, 1744784388, 3623814864, 7516104564
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OFFSET
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0,1
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COMMENTS
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It appears that the inequality a(n+1) > (2+2/n)*a(n) is true for n > 4.
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LINKS
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FORMULA
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EXAMPLE
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The values of the sigma_3 function (A001158) are increasing up to 25. Hence a(3)=24.
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MATHEMATICA
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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}]]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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