A319592 Decimal expansion of the probability that an integer 4-tuple is pairwise coprime.

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

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

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

Cf. A059956, A065473, A256392.

Sequence in context: A200628 A202245 A153258 * A200395 A064927 A343881

Adjacent sequences: A319589 A319590 A319591 * A319593 A319594 A319595

Keyword

nonn,cons

Author

Amiram Eldar, Aug 27 2019

Status

approved