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

Offset: 1

Author

Amiram Eldar, May 19 2020

Keywords

• nonn
• cons

Examples

			1.0827621932609245801221880381909265701843066555836...
		

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

• 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.
• 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.

Crossrefs

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

Cf. A236435, A236436.

Programs

Mathematica

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

PARI

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

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