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A085969 Decimal expansion of the prime zeta function at 9. 5
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

LINKS

Table of n, a(n) for n=0..104.

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. 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-Fran├žois Alcover, Feb 14 2013, from formula *)

RealDigits[ PrimeZetaP[ 9], 10, 111][[1]] (* Robert G. Wilson v, Sep 03 2014 *)

CROSSREFS

Cf. A085541, A085548, A085964 - A085968.

Sequence in context: A137505 A107498 A094295 * A117434 A115179 A131742

Adjacent sequences:  A085966 A085967 A085968 * A085970 A085971 A085972

KEYWORD

cons,nonn

AUTHOR

Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Jul 06 2003

STATUS

approved

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Last modified December 6 12:54 EST 2016. Contains 278781 sequences.