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A350299
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Numbers k > 1 with sigma(k)/(k * log(log(k))) > sigma(m)/(m * log(log(m))) for all m > k, sigma(k) being A000203(k), the sum of the divisors of k.
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1
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3, 4, 6, 12, 24, 60, 120, 180, 360, 2520, 5040
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OFFSET
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1,1
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COMMENTS
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Gronwall's theorem says that lim sup_{k -> infinity} sigma(k)/(k*log(log(k))) = exp(gamma). Moreover if the Riemann hypothesis is true, we have sigma(k)/(k*log(log(k))) < exp(gamma) when k > 5040 (gamma = Euler-Mascheroni constant).
The terms in the sequence listed above are provably correct since their ratios: sigma(k)/(k * log(log(k))) are greater than exp(gamma).
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REFERENCES
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Guy Robin, Grandes valeurs de la fonction somme des diviseurs et hypothèse de Riemann, J. Math. Pures Appl. 63 (1984), 187-213.
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LINKS
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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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