login
A335006
Decimal expansion of gamma - zeta'(2)/zeta(2), where gamma is the Euler-Mascheroni constant.
1
1, 1, 4, 7, 1, 7, 6, 6, 5, 7, 9, 9, 6, 0, 6, 5, 6, 6, 7, 0, 0, 6, 3, 7, 6, 4, 5, 0, 1, 0, 2, 1, 3, 2, 4, 3, 3, 4, 4, 5, 6, 4, 1, 6, 1, 6, 7, 4, 6, 8, 5, 4, 5, 7, 8, 3, 6, 3, 9, 6, 4, 5, 9, 5, 3, 2, 2, 7, 8, 5, 0, 0, 4, 1, 4, 4, 4, 0, 5, 2, 7, 7, 7, 2, 4, 8, 1
OFFSET
1,3
LINKS
Eckford Cohen, Arithmetical Functions of a Greatest Common Divisor. I, Proceedings of the American Mathematical Society, Vol. 11, No. 2 (1960), pp. 164-171.
FORMULA
Equals lim_{k->oo} zeta(2) * Sum_{i=1..k} phi(i)/i^2 - log(k), where phi is the Euler totient function (A000010).
EXAMPLE
1.1471766579960656670063764501021324334456416167468...
MATHEMATICA
RealDigits[EulerGamma - Zeta'[2]/Zeta[2], 10, 100][[1]]
PROG
(PARI) Euler - zeta'(2)/zeta(2) \\ Michel Marcus, May 19 2020
CROSSREFS
Cf. A000010 (phi), A001620 (gamma), A013661 (zeta(2)), A073002 (-zeta'(2)).
Sequence in context: A200355 A307868 A021216 * A085508 A198347 A371333
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, May 19 2020
STATUS
approved