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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

Table of n, a(n) for n=0..86.

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.)