login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A335004
Decimal expansion of 6*exp(gamma)/Pi^2.
1
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
1,3
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
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.
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
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. A001620 (gamma), A013661 (Pi^2/6), A051377 (esigma), A059956 (6/Pi^2), A073004 (exp(gamma)), A246499 (Pi^2/(6*exp(gamma))).
Sequence in context: A152179 A306339 A132716 * A134724 A269546 A248299
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, May 19 2020
STATUS
approved