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A065465
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Decimal expansion of product(1 - 1/(p^2*(p+1))), p prime >= 2).
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2
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8, 8, 1, 5, 1, 3, 8, 3, 9, 7, 2, 5, 1, 7, 0, 7, 7, 6, 9, 2, 8, 3, 9, 1, 8, 2, 2, 9, 0, 3, 2, 2, 7, 8, 4, 7, 1, 2, 9, 8, 6, 9, 2, 5, 7, 2, 0, 8, 0, 7, 6, 7, 3, 3, 6, 7, 0, 1, 6, 8, 5, 3, 5, 5, 4, 8, 6, 5, 7, 9, 0, 6, 3, 7, 9, 4, 1, 6, 9, 7, 4, 1, 0, 2, 2, 0, 4, 5, 5, 1, 7, 9, 7, 0, 2, 0, 9, 6
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OFFSET
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0,1
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LINKS
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Table of n, a(n) for n=0..97.
Eckford Cohen, Arithmetical functions associated with the unitary divisors of an integer, Math. Zeitschr. 74 (1960) 66-80.
S. R. Finch, Class number theory, page 7.
R. J. Mathar, Hardy-Littlewood constants embedded into infinite products..., arXiv:0903.2514 [math.NT], 2009-2011, Table 5, constant Q_1^(2).
G. Niklasch, Some number theoretical constants: 1000-digit values [Cached copy]
Simon Plouffe, Generalized expansions of real numbers, 2006
Eric Weisstein's World of Mathematics, Quadratic Class Number Constant
Eric Weisstein's World of Mathematics, Prime Products
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FORMULA
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sum_{n>=1} phi(n)/(n*J(n)) = (this constant)*A013661 with phi()=A000010() and J() = A007434() [Cohen, Corollary 5.1.1], - R. J. Mathar, Apr 11 2011
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EXAMPLE
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0.88151383972517077692839182290...
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MATHEMATICA
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$MaxExtraPrecision = 1000; digits = 98; terms = 1000; LR = Join[{0, 0, 0}, LinearRecurrence[{-2, -1, 1, 1}, {-3, 4, -5, 3}, terms+10]]; r[n_Integer] := LR[[n]]; Exp[NSum[r[n]*PrimeZetaP[n-1]/(n-1), {n, 4, terms}, NSumTerms -> terms, WorkingPrecision -> digits+10]] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Apr 16 2016 *)
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CROSSREFS
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Cf. A078087.
Sequence in context: A091648 A135707 A021923 * A265308 A199597 A197848
Adjacent sequences: A065462 A065463 A065464 * A065466 A065467 A065468
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KEYWORD
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cons,nonn
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AUTHOR
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N. J. A. Sloane, Nov 19 2001
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STATUS
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approved
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