This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A319593 #24 Jun 29 2023 09:03:19 %S A319593 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, %T A319593 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, %U A319593 7,3,7,2,1,4,2,7,3,8,5,3,2,0,9,4,0,6,1 %N A319593 Decimal expansion of the probability that an integer triple is pairwise unitary coprime. %C A319593 Two numbers are unitary coprime if their largest common unitary divisor is 1. %D A319593 Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, p. 54. %H A319593 László Tóth, <a href="https://doi.org/10.1007/978-1-4939-1106-6_19">Multiplicative arithmetic functions of several variables: a survey</a>, in Themistocles M. Rassias and Panos M. Pardalos (eds.), Mathematics Without Boundaries, Springer, New York, NY, 2014, pp. 483-514 (see p. 509), <a href="https://arxiv.org/abs/1310.7053">preprint</a>, arXiv:1310.7053 [math.NT], 2013-2014 (see p. 22). %F A319593 Equals 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). %e A319593 0.552306904157942811183227347309264708535455831404497... %t A319593 $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]] %o A319593 (PARI) zeta(2) * zeta(3) * prodeulerrat(1-4/p^2+7/p^3-9/p^4+8/p^5-2/p^6-3/p^7+2/p^8) \\ _Amiram Eldar_, Jun 29 2023 %Y A319593 Cf. A065473, A077610, A306071. %K A319593 nonn,cons %O A319593 0,1 %A A319593 _Amiram Eldar_, Aug 27 2019