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 A357330 #13 Feb 16 2025 08:34:04 %S A357330 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, %T A357330 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, %U A357330 7,0,4,6,9,5,5,7,6,9,5,2,2,9,7,7,9,3,4,2,3,5 %N A357330 Decimal expansion of sigma(N) / (N * log(log(N))) for N = 5040, where sigma = A000203. %C A357330 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 A357330 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RobinsTheorem.html">Robin's Theorem</a>. %H A357330 Wikipedia, <a href="https://en.wikipedia.org/wiki/Riemann_hypothesis#Growth_of_arithmetic_functions">Riemann hypothesis</a>. %F A357330 Equals 403 / (105 * log(log(5040))). %e A357330 sigma(5040) / (5040 * log(log(5040))) = 1.79097336653488113336... In comparison, exp(gamma) = 1.78107241799019798523... %t A357330 RealDigits[DivisorSigma[-1, 5040] / Log[Log[5040]], 10, 120][[1]] (* _Amiram Eldar_, Jun 19 2023 *) %o A357330 (PARI) sigma(5040) / (5040 * log(log(5040))) %Y A357330 Cf. A067698, A073004, A000203, A001620, A357331. %K A357330 nonn,cons %O A357330 1,2 %A A357330 _Jianing Song_, Sep 24 2022