OFFSET
0,1
COMMENTS
Constant is related to the asymptotics of A069205.
LINKS
Emil Grosswald, The average order of an arithmetic function, Duke Mathematical Journal, Vol. 23, No. 1 (1956), pp. 41-44. [constant C3]
EXAMPLE
0.8593922313585686897187145141861232817699609176983112114741634265903839649...
MATHEMATICA
ratfun = 1/((p-2)*(p-1)); zetas = 0; ratab = Table[konfun = Simplify[ratfun + c/(p^power - 1)] // Together; coefs = CoefficientList[Numerator[konfun], p]; sol = Solve[Last[coefs] == 0, c][[1]]; zetas = zetas + c*(Zeta'[power]/Zeta[power] + Log[2]/(2^power - 1)) /. sol; ratfun = konfun /. sol, {power, 2, 25}]; Do[Print[N[Sum[Log[p]*ratfun /. p -> Prime[k], {k, 2, m}] + zetas, 110]], {m, 2000, 10000, 2000}]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Aug 22 2021
STATUS
approved