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 A085969 Decimal expansion of the prime zeta function at 9. 13
 0, 0, 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 0,3 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 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 = 0..2003 H. Cohen, High Precision Computation of Hardy-Littlewood Constants, Preprint. 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>=2} 1/p^9 = Sum_{n=1..inf} mobius(n)*log(zeta(9*n))/n. 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 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. 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 STATUS approved

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