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

0,2

Comments

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

Links

Table of n, a(n) for n=0..101.

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.

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)

Example

0.18269074235035962468150918282692865988200290126984361751783...

Mathematica

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

Crossrefs

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

Sequence in context: A011468 A120219 A367899 * A377400 A199158 A086089

Adjacent sequences: A240973 A240974 A240975 * A240977 A240978 A240979

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Aug 07 2014

Status

approved