OFFSET
0,1
COMMENTS
This is the limit n -> infinity of (1/n^2)*Phi_1(n) = (1/n^2)*Sum_{k=1..n} psi(k), with Dedekind's psi function psi(k) = k*Product_{p|k} (1 + 1/p) = A001615(k). Distinct primes p dividing k appear, and the empty product for k = 1 is set to 1. See the Walfisz reference, Satz 2., p. 100 (with x -> n, and phi_1(n) = psi(n)).
REFERENCES
Arnold Walfisz, Weylsche Exponentialsummen in der neueren Zahlentheorie, VEB Deutscher Verlag der Wissenschaften, Berlin, 1963, p. 100, Satz 2.
LINKS
Eric Weisstein's World of Mathematics, Dedekind Function
Wikipedia, Dedekind psi function
FORMULA
Equal to 15/(2*Pi^2) = 1/((4/5)*zeta(2)), with 1/zeta(2) = A059956.
EXAMPLE
0.7599088773175332858290959740729572917826908100418491163420677392062984...
MATHEMATICA
RealDigits[15/2/Pi^2, 10, 100][[1]] (* Amiram Eldar, Sep 03 2019 *)
PROG
(PARI) 15/(2*Pi^2) \\ Felix Fröhlich, Sep 04 2019
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Sep 03 2019
STATUS
approved