A345364 Decimal expansion of Sum_{p primes} p * (log(p))^2 / (p-1)^3.

2, 0, 9, 1, 4, 8, 0, 2, 8, 2, 3, 4, 8, 9, 0, 1, 8, 5, 7, 3, 3, 8, 4, 0, 3, 6, 6, 4, 8, 0, 8, 6, 0, 5, 3, 4, 0, 1, 5, 4, 6, 3, 2, 2, 6, 1, 2, 3, 2, 4, 1, 8, 4, 2, 9, 9, 4, 0, 9, 1, 3, 5, 3, 2, 2, 2, 5, 6, 7, 2, 6, 4, 5, 3, 1, 1, 3, 5, 1, 4, 3, 6, 7, 6, 2, 6, 1, 8, 5, 4, 3, 4, 4, 5, 1, 4, 6, 9, 8, 9, 8, 7, 1, 5, 6

Offset

1,1

Links

Table of n, a(n) for n=1..105.

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

Cf. A085609, A306072, A335705, A335706, A335707, A345308.

Sequence in context: A238396 A247671 A011125 * A197583 A021831 A248897

Adjacent sequences: A345361 A345362 A345363 * A345365 A345366 A345367

Keyword

nonn,cons

Author

Vaclav Kotesovec, Jun 16 2021

Status

approved