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 A345308 #13 Feb 16 2025 08:34:02
%S A345308 1,2,2,6,9,6,8,8,0,5,6,5,3,4,7,0,0,0,5,9,6,5,6,6,2,5,6,8,7,4,5,7,6,2,
%T A345308 5,6,2,9,8,8,2,5,7,4,5,4,9,0,1,4,2,6,3,1,1,7,1,4,7,9,4,6,2,0,1,0,9,0,
%U A345308 0,3,1,4,1,3,0,9,2,6,6,0,6,1,9,4,1,1,4,4,3,4,5,7,0,5,9,7,8,9,9,5,7,0,6,2,6
%N A345308 Decimal expansion of Sum_{p primes} log(p) / (p-1)^2.
%H A345308 Steven R. Finch, <a href="https://doi.org/10.1017/9781316997741">Mathematical Constants II</a>, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 156 (constant C10 + 1).
%H A345308 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>, formula (13)-(14), (constant U).
%e A345308 1.226968805653470005965662568745762562988257454901426311714794620109...
%t A345308 ratfun = 1/((p - 1)^2); 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] /. sol; ratfun = konfun /. sol, {power, 2, 25}]; Do[Print[N[Sum[Log[p]*ratfun /. p -> Prime[k], {k, 1, m}] + zetas, 110]], {m, 1000, 5000, 1000}]
%Y A345308 Cf. A138312, A306016, A345364.
%K A345308 nonn,cons
%O A345308 1,2
%A A345308 _Vaclav Kotesovec_, Jun 13 2021