A347195 Decimal expansion of Sum_{primes p > 2} log(p) / ((p-2)*(p-1)).

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

Offset: 0

Author

Vaclav Kotesovec, Aug 22 2021

Keywords

• nonn
• cons

Comments

Constant is related to the asymptotics of A069205.

Examples

			0.8593922313585686897187145141861232817699609176983112114741634265903839649...
		

Links

• Emil Grosswald, The average order of an arithmetic function, Duke Mathematical Journal, Vol. 23, No. 1 (1956), pp. 41-44. [constant C3]

Crossrefs

Cf. A069205, A351347.

Programs

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}]