%I #34 Nov 05 2025 15:22:26

%S 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 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 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 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 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 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 Steven R. Finch, <a href="https://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, arXiv:2001.00578 [math.HO], 2020-2022, p. 17.

%H 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 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 Equals zeta(3)/(4*zeta(2)) = 3*zeta(3)/(2*Pi^2).

%F From _Amiram Eldar_, Jan 25 2024: (Start)

%F Equals (1/10) * Sum_{k>=1} A000188(k)/k^2.

%F Equals (1/10) * Sum_{k>=1} A048250(k)/k^3. (End)

%e 0.18269074235035962468150918282692865988200290126984361751783...

%t RealDigits[3*Zeta[3]/(2*Pi^2), 10, 102] // First

%Y Cf. A000188, A002117, A013662, A048250, A059956.

%K nonn,cons,easy

%O 0,2

%A _Jean-François Alcover_, Aug 07 2014