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A086242 Decimal expansion of sum 1/(p-1)^2 over primes p. 4
1, 3, 7, 5, 0, 6, 4, 9, 9, 4, 7, 4, 8, 6, 3, 5, 2, 8, 7, 9, 1, 7, 2, 5, 3, 1, 3, 0, 5, 2, 2, 4, 3, 9, 6, 9, 9, 1, 7, 9, 5, 9, 9, 9, 6, 0, 1, 7, 5, 3, 1, 7, 4, 5, 8, 7, 0, 9, 1, 8, 9, 3, 3, 5, 8, 9, 1, 2, 3, 5, 7, 1, 3, 1, 4, 1, 5, 5, 5, 2, 5, 5, 4, 2, 9, 9, 0, 7, 6, 5, 2, 4, 1, 6, 5, 8, 8, 1, 1, 4, 5, 2, 7, 6, 0, 6, 5, 7, 4, 4, 8, 0, 6, 5, 7, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, pp. 94-98.

LINKS

Table of n, a(n) for n=1..116.

Henri Cohen, High precision computation of Hardy-Littlewood Constants (dvi), 1998.

Eric Weisstein's World of Mathematics, Prime Sums

Eric Weisstein's World of Mathematics, Prime Factor

FORMULA

Sum_{k>=2} (k-1)*primezeta(k). - Robert Gerbicz, Sep 12 2012

EXAMPLE

1.37506499474863528791725313052243969917959996017...

MATHEMATICA

digits = 116; Np = NSum[(n-1)*PrimeZetaP[n], {n, 2, Infinity}, NSumTerms -> 3*digits, WorkingPrecision -> digits+10]; RealDigits[Np, 10, digits] // First (* Jean-Fran├žois Alcover, Sep 02 2015 *)

PROG

(PARI) default(realprecision, 256);

(f(k)=return(sum(n=1, 1024, moebius(n)/n*log(zeta(k*n)))));

sum(k=2, 1024, (k-1)*f(k)) /* Robert Gerbicz, Sep 12 2012 */

CROSSREFS

Sequence in context: A301755 A302558 A193506 * A096627 A065084 A132742

Adjacent sequences:  A086239 A086240 A086241 * A086243 A086244 A086245

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Jul 13 2003

EXTENSIONS

More digits copied from Cohen's paper by R. J. Mathar, Dec 05 2008

More terms from Robert Gerbicz, Sep 12 2012

STATUS

approved

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Last modified January 17 06:34 EST 2019. Contains 319207 sequences. (Running on oeis4.)