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A086242
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Decimal expansion of the sum of 1/(p-1)^2 over all primes p.
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13
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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
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OFFSET
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1,2
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REFERENCES
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Henri Cohen, Number Theory, Volume II: Analytic and Modern Tools, GTM Vol. 240, Springer, 2007; see pp. 208-209.
Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, Vol. 94, Cambridge University Press, 2003, pp. 94-98.
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LINKS
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Eric Weisstein's World of Mathematics, Prime Sums.
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FORMULA
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Equals Sum_{k>=2} (J_2(k)-phi(k)) * log(zeta(k)) / k, where J_2 = A007434 and phi = A000010 (Jakimczuk, 2017). - Amiram Eldar, Mar 18 2024
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EXAMPLE
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1.37506499474863528791725313052243969917959996017...
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MATHEMATICA
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digits = 116; Np = NSum[(n-1)*PrimeZetaP[n], {n, 2, Infinity}, NSumTerms -> 3*digits, WorkingPrecision -> digits+10]; RealDigits[Np, 10, digits] // First (* Jean-François Alcover, Sep 02 2015 *)
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PROG
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(PARI) default(realprecision, 256);
(f(k)=return(sum(n=1, 1024, moebius(n)/n*log(zeta(k*n)))));
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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More digits copied from Cohen's paper by R. J. Mathar, Dec 05 2008
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STATUS
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approved
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