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 A307715 #49 Apr 23 2025 10:22:58
%S A307715 9,7,7,1,8,9,1,8,3,2,6,8,9,3,6,5,5,4,4,5,7,8,8,5,7,4,9,4,7,6,4,3,4,7,
%T A307715 4,8,0,7,7,3,9,2,5,0,6,4,7,4,7,2,3,9,0,1,7,7,0,2,0,9,8,9,7,5,5,3,1,8,
%U A307715 4,4,5,2,9,3,9,2,3,9,3,3,5,6,2,9,0,1,2,3,2,1,0,7,9,7,4,3,2,0,3,3,5,9,2,3,2
%N A307715 Decimal expansion of Sum_{t>0} log((t + 1)/t)^2.
%C A307715 This constant appears at several places in the literature:
%C A307715 1) In the asymptotic formula of the number of minimal covering systems with exactly n elements (see Theorem 1.1 in Balister, Bollobás, Morris, Sahasrabudhe and Tiba) and
%C A307715 2) in the maximal size of the iterated divisor function
%C A307715 (see Theorem 1 in Buttkewitz, Elsholtz, Ford and Schlage-Puchta) and
%C A307715 3) in the maximal order of the iterated r_2 function, which counts the number of representations as sums of 2 squares (see Theorems 2.1. and 2.3 in Elsholtz, M. Technau and N. Technau). - Modified by _C. Elsholtz_, Apr 15 2025
%H A307715 P. Balister, B. Bollobás, R. Morris, J. Sahasrabudhe and M. Tiba, <a href="https://arxiv.org/abs/1904.04806">The structure and number of Erdős covering systems</a>, arXiv:1904.04806 [math.CO], 2019. J. Eur. Math. Soc. 26, 75-109 (2024).
%H A307715 Y. Buttkewitz, C. Elsholtz, K. Ford, and J.-C. Schlage-Puchta, <a href="https://arxiv.org/abs/1108.1815">The maximal order of iterated multiplicative functions</a>, arxiv:1108.1815 [math.NT], 2011. IMRN issue 17, 4051-4061 (2012).
%H A307715 C. Elsholtz, M. Technau, and N. Technau, <a href="https://arxiv.org/abs/1709.04799">The maximal order of iterated multiplicative functions</a>, arxiv:1709.04799 [math.NT], 2017. Mathematika, 65 (4) 2019, 990-1009.
%H A307715 P. Erdős, <a href="https://users.renyi.hu/~p_erdos/1952-03.pdf">Egy kongruenciarendszerekrol szóló problémáról</a>, (On a problem concerning congruence-systems, in Hungarian), Mat. Lapok, 4 (1952), 122-128.
%F A307715 From _Amiram Eldar_, Jun 17 2023: (Start)
%F A307715 Equals 2 * Sum_{k>=1} H(k) * (zeta(k+1)-1) / (k+1), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.
%F A307715 Equals -Sum_{k>=1} zeta'(2*k) / k. (End)
%e A307715 0.9771891832689365544578857494764347480773925064747239017702...
%t A307715 First[RealDigits[NSum[(Log[(t + 1)/t])^2, {t, 1, Infinity}, NSumTerms -> 100, Method -> {"NIntegrate", "MaxRecursion" -> 10}, WorkingPrecision -> 100]]]
%o A307715 (PARI) sumpos(t=1, log((t + 1)/t)^2) \\ _Michel Marcus_, Apr 26 2019
%Y A307715 Cf. A001008, A002805, A010553, A080340, A094076, A275489, A294593, A296195, A335831.
%K A307715 nonn,cons
%O A307715 0,1
%A A307715 _Stefano Spezia_, Apr 24 2019