login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A143524 Decimal expansion of the (negated) constant in the expansion of the prime zeta function about s = 1. 2
3, 1, 5, 7, 1, 8, 4, 5, 2, 0, 5, 3, 8, 9, 0, 0, 7, 6, 8, 5, 1, 0, 8, 5, 2, 5, 1, 4, 7, 3, 7, 0, 6, 5, 7, 1, 9, 9, 0, 5, 9, 2, 6, 8, 7, 6, 7, 8, 7, 2, 4, 3, 9, 2, 6, 1, 3, 7, 0, 3, 0, 2, 0, 9, 5, 9, 9, 4, 3, 2, 1, 5, 8, 8, 0, 2, 9, 6, 4, 6, 1, 2, 2, 2, 8, 0, 4, 4, 3, 1, 8, 5, 7, 5, 0, 0, 0, 9, 8, 4, 6, 3, 0, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

Henri Cohen, Number Theory, Volume II: Analytic and Modern Tools, GTM Vol. 240, Springer, 2007; see pp. 208-209.

LINKS

Table of n, a(n) for n=0..103.

Henri Cohen, High precision computation of Hardy-Littlewood constants, preprint, 1998.

Henri Cohen, High-precision computation of Hardy-Littlewood constants. [pdf copy, with permission]

Carl-Erik Fröberg, On the prime zeta function, BIT Numerical Mathematics, Vol. 8, No. 3 (1968), pp. 187-202.

R. J. Mathar, Series of reciprocal powers of k-almost primes, arXiv:0803.0900 [math.NT], 2008-2009, Table 2.

Eric Weisstein's World of Mathematics, Prime Zeta Function

Wikipedia, Prime zeta function.

FORMULA

Equals A077761 minus A001620. - R. J. Mathar, Jan 22 2009

From Amiram Eldar, Aug 08 2020: (Start)

Equals -Sum{k>=2} mu(k) * log(zeta(k)) / k.

Equals -Sum_{p prime} (1/p + log(1 - 1/p))

Equals Sum_{k>=2} P(k)/k, where P is the prime zeta function. (End)

EXAMPLE

-0.31571845194959281789...

MATHEMATICA

digits = 104; S = NSum[PrimeZetaP[n]/n, {n, 2, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 3*digits]; RealDigits[S, 10, digits] // First (* Jean-François Alcover, Sep 11 2015 *)

CROSSREFS

Sequence in context: A193844 A201552 A216182 * A134249 A188509 A265707

Adjacent sequences:  A143521 A143522 A143523 * A143525 A143526 A143527

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Aug 22 2008

EXTENSIONS

Digits changed to agree with A077761 and A001620 by R. J. Mathar, Oct 30 2009

Last digits corrected by Jean-François Alcover, Sep 11 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 28 09:53 EST 2021. Contains 340490 sequences. (Running on oeis4.)