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 A306016 Decimal expansion of -Zeta'(2)/Zeta(2). 3
 5, 6, 9, 9, 6, 0, 9, 9, 3, 0, 9, 4, 5, 3, 2, 8, 0, 6, 3, 9, 9, 8, 6, 4, 3, 6, 0, 0, 1, 9, 7, 3, 0, 0, 0, 2, 4, 0, 3, 4, 8, 2, 2, 8, 0, 8, 0, 6, 9, 3, 0, 9, 7, 9, 5, 5, 8, 1, 9, 7, 3, 6, 0, 4, 3, 7, 9, 1, 7, 2, 7, 7, 3, 6, 6, 7, 4, 0, 6, 0, 6, 7, 8, 7, 8, 6, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 179. J. B. Rosser, L. Schoenfeld, Approximate formulas for some functions of prime numbers, Ill. J. Math. 6 (1) (1962) 64-94, Table IV. FORMULA Equals -(6/Pi^2)*Zeta'(2). Equals 1 - 12*Zeta'(-1) - gamma - log(2*Pi). From Amiram Eldar, Aug 14 2020: (Start) Equals Sum_{k>=1} Lambda(k)/k^2, where Lambda is the Mangoldt function. Equals Sum_{p prime} log(p)/(p^2 - 1). (End) EXAMPLE Equals 0.569960993094532806399864360019730002403482280806930979558... MAPLE -(6/Pi^2)*Zeta(1, 2): evalf(%, 100); MATHEMATICA RealDigits[- Zeta'[2] / Zeta[2], 10, 87][[1]] PROG (PARI) -zeta'(2)/zeta(2) \\ Michel Marcus, Jan 11 2019 CROSSREFS Cf. A059956, A073002. Sequence in context: A021641 A332327 A260635 * A087176 A227006 A139454 Adjacent sequences:  A306013 A306014 A306015 * A306017 A306018 A306019 KEYWORD nonn,cons AUTHOR Peter Luschny, Jun 17 2018 STATUS approved

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Last modified September 24 05:29 EDT 2021. Contains 347623 sequences. (Running on oeis4.)