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 A380005 #12 Jan 15 2025 07:06:03 %S A380005 6,4,8,2,1,3,6,4,9,4,2,1,7,9,9,7,6,2,7,2,0,0,9,4,2,5,6,4,3,5,3,2,9,0, %T A380005 1,8,9,9,3,0,4,4,7,9,9,1,1,0,1,5,4,3,1,5,7,5,4,8,0,0,1,4,6,7,0,6,3,4, %U A380005 4,5,9,7,1,5,4,2,4,5,1,0,2,4,4,9,5,4,3,1,7,6 %N A380005 Decimal expansion of (7/3)*log(log(12)) - exp(gamma)*log(log(12))^2, where gamma is the Euler-Mascheroni constant (A001620). %C A380005 Theorem 2 in Robin (1984) states that, for n >= 3, sigma(n)/n <= exp(gamma)*log(log(n)) + c/log(log(n)), with equality for n = 12, where sigma is the sum-of-divisors function (A000203) and c is the constant given by the present sequence. Cf. also Weisstein, eqs. (29) - (33). %D A380005 G. Robin, Grandes valeurs de la fonction somme des diviseurs et hypothèse de Riemann, Journal de Mathématiques Pures et Appliquées, 63 (1984), pp. 187-213 (in French). See A073004 for a scanned copy. %H A380005 Paolo Xausa, <a href="/A380005/b380005.txt">Table of n, a(n) for n = 0..10000</a> %H A380005 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DivisorFunction.html">Divisor Function</a>, see eq. (31). %F A380005 Equals (7/3)*log(A016635) - A073004*log(A016635)^2. %e A380005 0.64821364942179976272009425643532901899304479911015... %t A380005 First[RealDigits[7/3*# - Exp[EulerGamma]*#^2, 10, 100]] & [Log[Log[12]]] %Y A380005 Cf. A000203, A001620, A016635, A058209, A073004. %K A380005 nonn,cons,easy %O A380005 0,1 %A A380005 _Paolo Xausa_, Jan 14 2025