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 A240976 #33 Jan 25 2024 02:44:58
%S A240976 1,8,2,6,9,0,7,4,2,3,5,0,3,5,9,6,2,4,6,8,1,5,0,9,1,8,2,8,2,6,9,2,8,6,
%T A240976 5,9,8,8,2,0,0,2,9,0,1,2,6,9,8,4,3,6,1,7,5,1,7,8,3,1,3,3,9,1,5,4,2,2,
%U A240976 6,9,0,7,6,6,9,6,2,1,3,9,2,0,6,6,7,6,7,5,0,9,2,8,5,2,4,6,9,7,5,8,2,2
%N A240976 Decimal expansion of 3*zeta(3)/(2*Pi^2), a constant appearing in the asymptotic evaluation of the average LCM of two integers chosen independently from the uniform distribution [1..n].
%C A240976 15*zeta(3)/Pi^2 = 10 * (this constant) equals the asymptotic mean of the abundancy index of the squares (Jakimczuk and Lalín, 2022). - _Amiram Eldar_, May 12 2023
%H A240976 Persi Diaconis and Paul Erdős, <a href="https://apps.dtic.mil/sti/citations/ADA048791">On the distribution of the greatest common divisor</a>, Technical Report No. 12 (1977) U.S. Army Research Office.
%H A240976 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, arXiv:2001.00578 [math.HO], 2020-2022, p. 17.
%H A240976 Rafael Jakimczuk and Matilde Lalín, <a href="https://doi.org/10.7546/nntdm.2022.28.4.617-634">Asymptotics of sums of divisor functions over sequences with restricted factorization structure</a>, Notes on Number Theory and Discrete Mathematics, Vol. 28, No. 4 (2022), pp. 617-634, eq. (4).
%H A240976 László Tóth, <a href="https://arxiv.org/abs/1310.7053">Multiplicative arithmetic functions of several variables: a survey</a>, arXiv:1310.7053 [math.NT], 2013-2014, formula (47), p. 23.
%F A240976 Equals zeta(3)/(4*zeta(2)) = 3*zeta(3)/(2*Pi^2).
%F A240976 From _Amiram Eldar_, Jan 25 2024: (Start)
%F A240976 Equals (1/10) * Sum_{k>=1} A000188(k)/k^2.
%F A240976 Equals (1/10) * Sum_{k>=1} A048250(k)/k^3. (End)
%e A240976 0.18269074235035962468150918282692865988200290126984361751783...
%t A240976 RealDigits[3*Zeta[3]/(2*Pi^2), 10, 102] // First
%Y A240976 Cf. A000188, A002117, A013662, A048250, A059956.
%K A240976 nonn,cons,easy
%O A240976 0,2
%A A240976 _Jean-François Alcover_, Aug 07 2014