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A319592
Decimal expansion of the probability that an integer 4-tuple is pairwise coprime.
2
1, 1, 4, 8, 8, 4, 0, 4, 4, 0, 8, 0, 2, 2, 8, 7, 8, 8, 7, 2, 9, 2, 5, 1, 2, 7, 6, 7, 0, 1, 5, 9, 9, 0, 9, 7, 8, 4, 8, 7, 1, 3, 5, 5, 2, 6, 8, 7, 2, 8, 3, 0, 1, 7, 6, 2, 4, 8, 4, 8, 4, 2, 7, 0, 6, 2, 5, 6, 6, 6, 7, 2, 8, 0, 1, 6, 1, 6, 7, 4, 6, 1, 7, 4, 0, 2, 3
OFFSET
0,3
LINKS
László Tóth, The probability that k positive integers are pairwise relatively prime, Fibonacci Quarterly, Vol. 40, No. 1 (2002), pp. 13-18.
FORMULA
Equals Product_{p prime} (1 - 1/p)^3 * (1 + 3/p).
EXAMPLE
0.114884044080228788729251276701599097848713552687283...
MATHEMATICA
$MaxExtraPrecision = 1000; nm = 1000; c = LinearRecurrence[{-2, 3}, {0, -12}, nm]; f[x_] := (1 - x)^3*(1 + 3*x); RealDigits[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]]
PROG
(PARI) prodeulerrat((1 - 1/p)^3 * (1 + 3/p)) \\ Amiram Eldar, Jun 29 2023
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Aug 27 2019
STATUS
approved