A335004 Decimal expansion of 6*exp(gamma)/Pi^2.

1, 0, 8, 2, 7, 6, 2, 1, 9, 3, 2, 6, 0, 9, 2, 4, 5, 8, 0, 1, 2, 2, 1, 8, 8, 0, 3, 8, 1, 9, 0, 9, 2, 6, 5, 7, 0, 1, 8, 4, 3, 0, 6, 6, 5, 5, 5, 8, 3, 6, 0, 0, 1, 4, 4, 1, 0, 2, 0, 3, 1, 9, 7, 4, 3, 5, 5, 1, 2, 8, 6, 1, 9, 2, 9, 8, 2, 9, 5, 0, 4, 3, 4, 2, 4, 2, 2, 0, 6, 2, 1, 4, 3, 2, 4, 1, 9, 2, 1, 8, 6, 6, 4, 5, 8

Offset

1,3

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.5.1, p. 31.

József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, chapter III, page 100.

Links

Table of n, a(n) for n=1..105.

J. Fabrykowski and M. V. Subbarao, The maximal order and the average order of multiplicative function sigma^(e)(n), in Jean M. de Koninck and Claude Levesque (eds.), Théorie des nombres/Number theory: Proceedings of the International Number Theory Conference held at Université Laval, July 5-18, 1987, Berlin, New York: de Gruyter, 1989, pp. 201-206.

Rafael Jakimczuk, h-free numbers. The function sigma(n), Researchgate, 2025. See Theorem 1.1, p. 2.

Florian Luca and Carl Pomerance, On some problems of Mąkowski-Schinzel and Erdős concerning the arithmetical functions phi and sigma, Colloquium Mathematicum, Vol. 92 (2002), pp. 111-130.

Michel Planat, Riemann hypothesis from the Dedekind psi function, arXiv:1010.3239 [math.GM], 2010.

Formula

Equals limsup_{k->oo} esigma(k)/(k*log(log(k))), where esigma(k) is the sum of exponential divisors of k (A051377).

Equals A073004 * A059956 = A073004 / A013661 = 1 / A246499.

Equals lim_{k->oo} (1/log(k)) * Product_{p prime <= k} (1 + 1/p). - Amiram Eldar, Jul 09 2020

Equals limsup_{k->oo} sigma(k)/(k * log(log(k))), where k runs over the squarefree numbers (Jakimczuk, 2025). - Amiram Eldar, Sep 19 2025

Example

1.0827621932609245801221880381909265701843066555836...

Mathematica

RealDigits[6*Exp[EulerGamma]/Pi^2, 10, 100][[1]]

Prog

(PARI) 6*exp(Euler)/Pi^2 \\ Michel Marcus, May 19 2020

Crossrefs

Cf. A000203 (sigma), A001620 (gamma), A005117, A013661 (Pi^2/6), A051377 (esigma), A059956 (6/Pi^2), A073004 (exp(gamma)), A246499 (Pi^2/(6*exp(gamma))).

Cf. A236435, A236436.

Sequence in context: A152179 A306339 A132716 * A134724 A269546 A392514

Adjacent sequences: A335001 A335002 A335003 * A335005 A335006 A335007

Keyword

nonn,cons

Author

Amiram Eldar, May 19 2020

Extensions

More terms from Amiram Eldar, Sep 19 2025

Status

approved