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A357330 Decimal expansion of sigma(N) / (N * log(log(N))) for N = 5040, where sigma = A000203. 1
1, 7, 9, 0, 9, 7, 3, 3, 6, 6, 5, 3, 4, 8, 8, 1, 1, 3, 3, 3, 6, 1, 9, 0, 1, 3, 5, 0, 5, 9, 1, 0, 9, 5, 1, 7, 4, 0, 9, 0, 9, 5, 3, 9, 0, 7, 9, 8, 7, 5, 7, 3, 5, 7, 7, 9, 1, 7, 4, 6, 5, 3, 5, 2, 3, 5, 6, 6, 7, 0, 4, 6, 9, 5, 5, 7, 6, 9, 5, 2, 2, 9, 7, 7, 9, 3, 4, 2, 3, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
It is known that the Riemann Hypothesis (RH) is true if and only if sigma(n) < exp(gamma) * n * log(log(n)) for all n > 5040, where gamma = A001620 is the Euler-Mascheroni constant; that is to say, the RH is true if and only if 5040 is the last term in A067698.
LINKS
Eric Weisstein's World of Mathematics, Robin's Theorem.
Wikipedia, Riemann hypothesis.
FORMULA
Equals 403 / (105 * log(log(5040))).
EXAMPLE
sigma(5040) / (5040 * log(log(5040))) = 1.79097336653488113336... In comparison, exp(gamma) = 1.78107241799019798523...
MATHEMATICA
RealDigits[DivisorSigma[-1, 5040] / Log[Log[5040]], 10, 120][[1]] (* Amiram Eldar, Jun 19 2023 *)
PROG
(PARI) sigma(5040) / (5040 * log(log(5040)))
CROSSREFS
Sequence in context: A104757 A199392 A120670 * A175638 A091900 A222135
KEYWORD
nonn,cons
AUTHOR
Jianing Song, Sep 24 2022
STATUS
approved

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Last modified April 23 20:33 EDT 2024. Contains 371916 sequences. (Running on oeis4.)