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 A319593 Decimal expansion of the probability that an integer triple is pairwise unitary coprime. 0
 5, 5, 2, 3, 0, 6, 9, 0, 4, 1, 5, 7, 9, 4, 2, 8, 1, 1, 1, 8, 3, 2, 2, 7, 3, 4, 7, 3, 0, 9, 2, 6, 4, 7, 0, 8, 5, 3, 5, 4, 5, 5, 8, 3, 1, 4, 0, 4, 4, 9, 7, 6, 0, 7, 3, 3, 0, 2, 2, 7, 0, 0, 8, 0, 1, 5, 5, 3, 7, 3, 7, 2, 1, 4, 2, 7, 3, 8, 5, 3, 2, 0, 9, 4, 0, 6, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Two numbers are unitary coprime if their largest common unitary divisor is 1. REFERENCES Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, p. 54. LINKS László Tóth, Multiplicative arithmetic functions of several variables: a survey, in Themistocles M. Rassias and Panos M. Pardalos (eds.), Mathematics Without Boundaries, Springer, New York, NY, 2014, pp. 483-514 (see p. 509), preprint, arXiv:1310.7053 [math.NT] (2014) (see p. 22). FORMULA zeta(2) * zeta(3) * Product_{p prime} (1 - 4/p^2 + 7/p^3 - 9/p^4 + 8/p^5 - 2/p^6 - 3/p^7 + 2/p^8). EXAMPLE 0.552306904157942811183227347309264708535455831404497... MATHEMATICA \$MaxExtraPrecision = 1000; nm = 1000; f[x_] := 1 - 4*x^2 + 7*x^3 - 9*x^4 + 8*x^5 - 2*x^6 - 3*x^7 + 2*x^8; c = LinearRecurrence[{-1, 3, -4, 5, -3, -1, 2}, {0, -8, 21, -68, 180, -503, 1428}, nm]; RealDigits[f[1/2] * f[1/3] * Zeta[2] * Zeta[3] * Exp[NSum[Indexed[c, k]*(PrimeZetaP[k] - 1/2^k - 1/3^k)/k, {k, 2, nm}, NSumTerms -> nm, WorkingPrecision -> nm]], 10, 100][[1]] CROSSREFS Cf. A065473, A077610, A306071. Sequence in context: A319305 A196614 A319905 * A335321 A172125 A125642 Adjacent sequences:  A319590 A319591 A319592 * A319594 A319595 A319596 KEYWORD nonn,cons AUTHOR Amiram Eldar, Aug 27 2019 STATUS approved

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Last modified August 2 05:02 EDT 2021. Contains 346409 sequences. (Running on oeis4.)