OFFSET
1,1
COMMENTS
Evaluated from Sum_{m,k >= 1} A008683(k)*I(k*m)/k^2, where I(x) = Integral_{t=x..infinity} log zeta(t) dt is Cohen's underivative.
REFERENCES
Henri Cohen, Number Theory, Volume II: Analytic and Modern Tools, GTM Vol. 240, Springer, 2007; see pp. 208-209.
LINKS
D. A. Clark, An upper bound of sum 1/(a_i log a_i) for quasi-primitive sequences, Comp. Math. Appl., 35 (1998), 105-109.
H. Cohen, High precision computation of Hardy-Littlewood constants, preprint, 1998.
Henri Cohen, High-precision computation of Hardy-Littlewood constants. [pdf copy, with permission]
R. J. Mathar, Twenty digits of some Integrals of the Prime Zeta Function, arXiv:0811.4739 [math.NT].
FORMULA
Equals Sum_{p primes} -log(1-1/p)/log(p). - Vaclav Kotesovec, Jun 12 2022
EXAMPLE
2.0066664528310687...
PROG
(PARI) default(realprecision, 200); su = 0; for(s=1, 400, su = su + sum(k=1, 500, moebius(k)/k^2 * intnum(x=s*k, [[1], 1], log(zeta(x))))/s; print(su)); \\ Vaclav Kotesovec, Jun 12 2022
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
R. J. Mathar, Mar 09 2008
EXTENSIONS
8 more digits from R. J. Mathar, Dec 04 2008
More terms from Vaclav Kotesovec, Jun 12 2022
STATUS
approved