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A350299 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. 1
3, 4, 6, 12, 24, 60, 120, 180, 360, 2520, 5040 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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).
REFERENCES
Guy Robin, Grandes valeurs de la fonction somme des diviseurs et hypothèse de Riemann, J. Math. Pures Appl. 63 (1984), 187-213.
LINKS
Keith Briggs, Abundant numbers and the Riemann Hypothesis, Experimental Math., Vol. 16 (2006), pp. 251-256.
S. Nazardonyavi and S. Yakubovich, Extremely Abundant Numbers and the Riemann Hypothesis, Journal of Integer Sequences, 17 (2014), Article 14.2.8.
Thomas Strohmann, C++ code
CROSSREFS
Cf. also A001620, A073004.
Sequence in context: A358358 A160684 A176045 * A255733 A137333 A006719
KEYWORD
nonn
AUTHOR
Thomas Strohmann, Dec 23 2021
STATUS
approved

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Last modified June 22 15:57 EDT 2024. Contains 373590 sequences. (Running on oeis4.)