

A136271


Decimal expansion of sum log(p)/p^2 over the primes p=2,3,5,7,11,...


9



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

0,1


COMMENTS

The negative first derivative of the Prime Zeta function at 2.


REFERENCES

Henri Cohen, Number Theory, Volume II: Analytic and Modern Tools, GTM Vol. 240, Springer, 2007; see pp. 208209.


LINKS

Table of n, a(n) for n=0..103.
Henri Cohen, Highprecision computation of HardyLittlewood constants, preprint 1998.
Henri Cohen, Highprecision computation of HardyLittlewood constants. [pdf copy, with permission]
R. J. Mathar, Series of reciprocal powers of kalmost primes, arXiv:0803.0900 [math.NT], Table 2.
J. B. Rosser, L. Schoenfeld, Approximate formulas for some functions of prime numbers, Ill. J. Math. 6 (1) (1962) 6494, Table IV


FORMULA

Equals Sum_{n >= 1} log(A000040(n))/A001248(n).


EXAMPLE

0.4930911093687...


MATHEMATICA

RealDigits[PrimeZetaP'[2], 10, 104] // First (* JeanFrançois Alcover, Sep 11 2015 *)


CROSSREFS

Cf. A303493A303499.
Sequence in context: A011262 A073843 A073842 * A113970 A021957 A096301
Adjacent sequences: A136268 A136269 A136270 * A136272 A136273 A136274


KEYWORD

cons,nonn


AUTHOR

R. J. Mathar, Mar 09 2008


EXTENSIONS

Removed 6 digits where preprints disagree. Added zero to an Anumber in formula. Corrected Cohen preprint year. Added 2nd link.  R. J. Mathar, Nov 27 2008
More digits from JeanFrançois Alcover, Sep 11 2015


STATUS

approved



