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 A320027 Decimal expansion of the probability that an integer 4-tuple is pairwise unitary coprime. 0
 1, 3, 7, 3, 1, 0, 6, 5, 1, 8, 0, 9, 0, 7, 3, 5, 9, 1, 8, 7, 1, 5, 8, 7, 4, 7, 0, 6, 1, 2, 4, 3, 5, 0, 1, 2, 3, 1, 9, 8, 5, 4, 4, 7, 2, 2, 1, 4, 5, 1, 6, 1, 5, 4, 3, 9, 9, 3, 9, 4, 4, 4, 4, 1, 5, 0, 4, 5, 6, 8, 1, 9, 6, 2, 8, 9, 6, 0, 8, 2, 7, 5, 7, 5, 4, 5, 6 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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)^2 * zeta(3) * zeta(4) * Product_{p prime} (1 - 8/p^2 + 3/p^3 + 27/p^4 - 24/p^5 - 14/p^6 - 3/p^7 + 37/p^8 - 30/p^9 + 42/p^10 - 33/p^11 - 41/p^12 + 78/p^13 - 44/p^14 + 9/p^15). EXAMPLE 0.137310651809073591871587470612435012319854472214516... MATHEMATICA \$MaxExtraPrecision = 1000; nm = 1000; f[x_] := 1 - 8*x^2 + 3*x^3 + 27*x^4 - 24*x^5 - 14*x^6 - 3*x^7 + 37*x^8 - 30*x^9 + 42*x^10 - 33*x^11 - 41*x^12 + 78*x^13 - 44*x^14 + 9*x^15; c = LinearRecurrence[{-3, 2, 11, -3, -16, -14, 6, 7, 19, 0, -17, 9}, {0, -16, 9, -20, 0, 161, -588, 2116, -5859, 15104, -34716, 70609}, nm]; RealDigits[Zeta[2]^2*Zeta[3]*Zeta[4]*f[1/2]*f[1/3]*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. A077610, A306071, A319592. Sequence in context: A248214 A144713 A233380 * A134731 A133368 A153027 Adjacent sequences:  A320024 A320025 A320026 * A320028 A320029 A320030 KEYWORD nonn,cons AUTHOR Amiram Eldar, Aug 27 2019 STATUS approved

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Last modified February 22 13:51 EST 2020. Contains 332136 sequences. (Running on oeis4.)