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 A085969 Decimal expansion of the prime zeta function at 9. 18
 2, 0, 0, 4, 4, 6, 7, 5, 7, 4, 9, 6, 2, 4, 5, 0, 6, 6, 3, 0, 7, 3, 5, 8, 5, 1, 4, 0, 7, 8, 3, 1, 1, 7, 5, 3, 6, 8, 2, 2, 9, 2, 0, 3, 4, 9, 7, 3, 8, 5, 7, 8, 5, 5, 0, 2, 7, 5, 5, 9, 1, 7, 3, 9, 7, 9, 3, 7, 2, 6, 2, 5, 1, 5, 1, 9, 9, 7, 7, 1, 9, 0, 8, 1, 3, 5, 5, 3, 4, 3, 4, 0, 1, 2, 4, 4, 1, 7, 7, 2, 4, 3, 0 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET -2,1 COMMENTS Mathar's Table 1 (cited below) lists expansions of the prime zeta function at integers s in 10..39. - Jason Kimberley, Jan 07 2017 REFERENCES Henri Cohen, Number Theory, Volume II: Analytic and Modern Tools, GTM Vol. 240, Springer, 2007; see pp. 208-209. J. W. L. Glaisher, On the Sums of Inverse Powers of the Prime Numbers, Quart. J. Math. 25, 347-362, 1891. LINKS Jason Kimberley, Table of n, a(n) for n = -2..1999 Henri Cohen, High Precision Computation of Hardy-Littlewood Constants, Preprint, 1998. Henri Cohen, High-precision computation of Hardy-Littlewood constants. [pdf copy, with permission] X. Gourdon and P. Sebah, Some Constants from Number theory R. J. Mathar, Series of reciprocal powers of k-almost primes, arXiv:0803.0900 [math.NT], 2008-2009. Table 1. Eric Weisstein's World of Mathematics, Prime Zeta Function FORMULA P(9) = Sum_{p prime} 1/p^9 = Sum_{n=1..inf} mobius(n)*log(zeta(9*n))/n. Equals Sum_{k>=1} 1/A179665(k). - Amiram Eldar, Jul 27 2020 EXAMPLE 0.0020044675749624506630... MAPLE A085969:= proc(i) print(evalf(add(1/ithprime(k)^9, k=1..i), 100)); end: A085969(100000); # Paolo P. Lava, May 29 2012 MATHEMATICA pz9[n_] := pz9[n] = Join[{0, 0}, Sum[ MoebiusMu[k]*Log[Zeta[9*k]]/k, {k, 1, n}] // RealDigits[#, 10, 103]& // First]; pz9[100]; pz9[n = 200]; While[pz9[n] != pz9[n - 100], n = n + 100]; pz9[n] (* Jean-François Alcover, Feb 14 2013, from formula *) RealDigits[ PrimeZetaP[ 9], 10, 111][[1]] (* Robert G. Wilson v, Sep 03 2014 *) PROG (MAGMA) R := RealField(106); PrimeZeta := func; [0, 0] cat Reverse(IntegerToSequence(Floor(PrimeZeta(9, 38)*10^105))); // Jason Kimberley, Dec 30 2016 (PARI) sumeulerrat(1/p, 9) \\ Hugo Pfoertner, Feb 03 2020 CROSSREFS Decimal expansion of the prime zeta function: A085548 (at 2), A085541 (at 3), A085964 (at 4) to A085968 (at 8), this sequence (at 9). Cf. A013667, A179665. Sequence in context: A137505 A107498 A094295 * A117434 A115179 A131742 Adjacent sequences:  A085966 A085967 A085968 * A085970 A085971 A085972 KEYWORD cons,easy,nonn AUTHOR Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jul 06 2003 EXTENSIONS Changed offset and adapted data by Hugo Pfoertner, Jan 31 2020 STATUS approved

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Last modified December 1 22:24 EST 2020. Contains 338858 sequences. (Running on oeis4.)