OFFSET
0,1
LINKS
Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 51 (constant Y2).
V. Sita Ramaiah and D. Suryanarayana, Sums of reciprocals of some multiplicative functions, Mathematical Journal of Okayama University, Vol. 21, No. 2 (1979), pp. 161-162, formula (4.1)-(4.4).
László Tóth, Alternating sums concerning multiplicative arithmetic functions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1 (section 4.3, p. 18).
FORMULA
EXAMPLE
0.5073388825830843781004978765159526773890196348281644808049...
MATHEMATICA
$MaxExtraPrecision = 1000; Do[ratfun = (p - 1)^2 * Sum[j/(p^j - 1)/(p^(j + 1) - 1), {j, 1, m}]/(p*(1 - (p - 1)^2/p * Sum[1/(p^j - 1)/(p^(j + 1) - 1), {j, 1, m}])); zetas = 0; ratab = Table[konfun = Together[ratfun + c/(p^power - 1)]; coefs = CoefficientList[Numerator[konfun], p]; sol = Solve[Last[coefs] == 0, c][[1]]; zetas = zetas + c*Zeta'[power]/Zeta[power] /. sol; ratfun = konfun /. sol, {power, 2, 40}]; Print[N[Sum[Log[p]*ratfun /. p -> Prime[k], {k, 1, m}] + zetas, 110]], {m, 10, 250, 10}]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Jun 14 2021
STATUS
approved