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A222056
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Decimal expansion of (6/Pi^2)*Sum_{n>=1} 1/prime(n)^2.
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4
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2, 7, 4, 9, 3, 3, 4, 6, 3, 3, 8, 6, 5, 2, 5, 5, 8, 8, 9, 1, 7, 5, 3, 8, 7, 3, 8, 7, 2, 2, 6, 7, 9, 3, 5, 6, 9, 0, 9, 8, 1, 6, 4, 6, 1, 9, 7, 5, 8, 6, 2, 3, 5, 1, 7, 8, 9, 8, 6, 0, 3, 4, 4, 7, 3, 6, 2, 4, 1, 6, 3, 1, 7, 2, 0, 3, 1, 7, 5, 7, 6, 9, 4, 1, 5, 6, 1, 2, 7, 3, 8, 3, 2, 1, 8, 7, 1, 2, 2, 4, 9, 0
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OFFSET
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0,1
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COMMENTS
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This is the probability that the gcd of any two integers is prime. - David Cushing, Mar 27 2013
The asymptotic density of integers whose largest square divisor is a square of a prime (A082293). - Amiram Eldar, Jul 07 2020
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LINKS
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EXAMPLE
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0.27493346338652558891753873872267935690981646197586235178986...
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MATHEMATICA
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Drop[Flatten[RealDigits[N[PrimeZetaP[2] 6/Pi^2, 100]]], -1] (* Geoffrey Critzer, Jan 17 2015 *)
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PROG
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(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))))
(PARI) sumeulerrat(1/p, 2)/zeta(2) \\ Amiram Eldar, Mar 18 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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