cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A357331 Decimal expansion of sigma(N) / (exp(gamma) * N * log(log(N))) for N = 5040, where sigma = A000203 and gamma = A001620 is the Euler-Mascheroni constant.

Original entry on oeis.org

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Offset: 1

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Author

Jianing Song, Sep 24 2022

Keywords

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.

Examples

			sigma(5040) / (exp(gamma) * 5040 * log(log(5040))) = 1.00555898145672010364... > 1.
		

Crossrefs

Programs

  • Mathematica
    RealDigits[DivisorSigma[-1, 5040] / (Exp[EulerGamma] * Log[Log[5040]]), 10, 120][[1]] (* Amiram Eldar, Jun 19 2023 *)
  • PARI
    sigma(5040) / (exp(Euler) * 5040 * log(log(5040)))

Formula

Equals 403 / (exp(gamma) * 105 * log(log(5040))).
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