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.
%I A357331 #15 Feb 16 2025 08:34:04 %S A357331 1,0,0,5,5,5,8,9,8,1,4,5,6,7,2,0,1,0,3,6,4,2,4,7,0,7,6,7,7,8,1,5,5,4, %T A357331 4,3,1,6,9,8,4,4,3,0,1,4,6,7,4,1,5,2,7,9,7,3,6,8,0,2,5,8,3,2,2,5,7,4, %U A357331 6,5,9,5,4,9,5,5,8,5,2,2,7,8,7,7,1,4,6,2,3,9 %N 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. %C A357331 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. %H A357331 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RobinsTheorem.html">Robin's Theorem</a>. %H A357331 Wikipedia, <a href="https://en.wikipedia.org/wiki/Riemann_hypothesis#Growth_of_arithmetic_functions">Riemann hypothesis</a>. %F A357331 Equals 403 / (exp(gamma) * 105 * log(log(5040))). %e A357331 sigma(5040) / (exp(gamma) * 5040 * log(log(5040))) = 1.00555898145672010364... > 1. %t A357331 RealDigits[DivisorSigma[-1, 5040] / (Exp[EulerGamma] * Log[Log[5040]]), 10, 120][[1]] (* _Amiram Eldar_, Jun 19 2023 *) %o A357331 (PARI) sigma(5040) / (exp(Euler) * 5040 * log(log(5040))) %Y A357331 Cf. A067698, A073004, A000203, A001620, A357330. %K A357331 nonn,cons %O A357331 1,4 %A A357331 _Jianing Song_, Sep 24 2022