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].
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, 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, 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
Offset: 0
Examples
0.18269074235035962468150918282692865988200290126984361751783...
Links
- Persi Diaconis and Paul Erdős, On the distribution of the greatest common divisor, Technical Report No. 12 (1977) U.S. Army Research Office.
- Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020-2022, p. 17.
- Rafael Jakimczuk and Matilde Lalín, Asymptotics of sums of divisor functions over sequences with restricted factorization structure, Notes on Number Theory and Discrete Mathematics, Vol. 28, No. 4 (2022), pp. 617-634, eq. (4).
- László Tóth, Multiplicative arithmetic functions of several variables: a survey, arXiv:1310.7053 [math.NT], 2013-2014, formula (47), p. 23.
Programs
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Mathematica
RealDigits[3*Zeta[3]/(2*Pi^2), 10, 102] // First
Formula
Equals zeta(3)/(4*zeta(2)) = 3*zeta(3)/(2*Pi^2).
From Amiram Eldar, Jan 25 2024: (Start)
Equals (1/10) * Sum_{k>=1} A000188(k)/k^2.
Equals (1/10) * Sum_{k>=1} A048250(k)/k^3. (End)
Comments