This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A345364 #7 Feb 16 2025 08:34:02
%S A345364 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,
%T A345364 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,
%U A345364 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
%N A345364 Decimal expansion of Sum_{p primes} p * (log(p))^2 / (p-1)^3.
%H A345364 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>, formula (15)-(16), (constant V).
%e A345364 2.0914802823489018573384036648086053401546322612324184299409135322256726453113...
%t A345364 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}]
%Y A345364 Cf. A085609, A306072, A335705, A335706, A335707, A345308.
%K A345364 nonn,cons
%O A345364 1,1
%A A345364 _Vaclav Kotesovec_, Jun 16 2021