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A154945 Decimal expansion of sum_p 1/(p^2-1), summed over the primes p = A000040. 10
5, 5, 1, 6, 9, 3, 2, 9, 7, 6, 5, 6, 9, 9, 9, 1, 8, 4, 4, 3, 9, 7, 3, 1, 0, 2, 3, 9, 7, 1, 3, 4, 3, 5, 7, 8, 1, 3, 1, 5, 0, 0, 3, 7, 7, 7, 7, 8, 6, 2, 8, 2, 5, 2, 2, 3, 0, 6, 1, 7, 3, 3, 4, 0, 5, 9, 5, 6, 5, 5, 9, 7, 6, 4, 1, 0, 7, 0, 6, 7, 1, 0, 7, 7, 7, 5, 0, 9, 8, 3, 1, 6, 8, 2, 7, 7, 9, 6, 0, 7, 2, 5, 0, 5, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

By geometric series expansion, the same as the sum over the prime zeta function at even arguments, P(2i), i=1,2,....

(Pi^2/6)*density of A190641, the numbers divisible by exactly one prime with exponent greater than 1. - Charles R Greathouse IV, Aug 02 2016

LINKS

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

J. Grah, Comportement moyen du cardinal de certains ensembles de facteurs premiers, Monatsh. Math. 118 (1994) 91-109, Corollary 6.1.

Carl Pomerance, Andrzej Schinzel, Multiplicative Properties of Sets of Residues, Moscow Journal of Combinatorics and Number Theory. 2011. Vol. 1. Iss. 1. pp. 52-66. See p. 61.

FORMULA

Equals Sum_{k>=1} 1/A084920(k) = Sum_{i>=1} P(2i) = A085548+A085964+A085966+A085968+... = A152447+A085548-A154932.

EXAMPLE

0.551693297656999184439731023971343578131500377778628252230...

MATHEMATICA

digits = 105; m0 = 2 digits; Clear[rd]; rd[m_] := rd[m] = RealDigits[delta1 = Sum[PrimeZetaP[2n], {n, 1, m}] , 10, digits][[1]]; rd[m0]; rd[m = 2m0];

While[rd[m] != rd[m-m0], Print[m]; m = m+m0]; Print[N[delta1, digits]]; rd[m] (* Jean-François Alcover, Sep 11 2015, updated Mar 16 2019 *)

PROG

(PARI) eps()=2.>>bitprecision(1.)

primezeta(s)=my(t=s*log(2)); sum(k=1, lambertw(t/eps())\t, moebius(k)/k*log(abs(zeta(k*s))))

sumpos(n=1, primezeta(2*n)) \\ Charles R Greathouse IV, Aug 02 2016

CROSSREFS

Sequence in context: A082956 A190101 A097566 * A300710 A254347 A011094

Adjacent sequences:  A154942 A154943 A154944 * A154946 A154947 A154948

KEYWORD

cons,nonn

AUTHOR

R. J. Mathar, Jan 17 2009

EXTENSIONS

More digits from Jean-François Alcover, Sep 11 2015

STATUS

approved

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Last modified February 25 20:04 EST 2020. Contains 332258 sequences. (Running on oeis4.)