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A347195
Decimal expansion of Sum_{primes p > 2} log(p) / ((p-2)*(p-1)).
3
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
0,1
COMMENTS
Constant is related to the asymptotics of A069205.
LINKS
Emil Grosswald, The average order of an arithmetic function, Duke Mathematical Journal, Vol. 23, No. 1 (1956), pp. 41-44. [constant C3]
EXAMPLE
0.8593922313585686897187145141861232817699609176983112114741634265903839649...
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}]
CROSSREFS
Sequence in context: A233033 A244810 A273985 * A132036 A132717 A200487
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Aug 22 2021
STATUS
approved