OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Prime Factor, formula (15)-(16), (constant V).
EXAMPLE
2.0914802823489018573384036648086053401546322612324184299409135322256726453113...
MATHEMATICA
ratfun = p/(p - 1)^3; zetas = 0; ratab = Table[konfun = Together[Simplify[ratfun - c*(p^power/(p^power - 1)^2)]]; coefs = CoefficientList[Numerator[konfun], p]; sol = Solve[Last[coefs] == 0, c][[1]]; zetas = zetas + c*(-Zeta'[power]^2 / Zeta[power]^2 + Zeta''[power] / Zeta[power]) /. sol; ratfun = konfun /. sol, {power, 2, 30}]; Do[Print[N[Sum[Log[p]^2*ratfun /. p -> Prime[k], {k, 1, m}] + zetas, 110]], {m, 100, 1000, 100}]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Jun 16 2021
STATUS
approved