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

Author

Amiram Eldar, Aug 27 2019

Keywords

• nonn
• cons

Examples

			0.114884044080228788729251276701599097848713552687283...
		

Links

• László Tóth, The probability that k positive integers are pairwise relatively prime, Fibonacci Quarterly, Vol. 40, No. 1 (2002), pp. 13-18.

Crossrefs

Cf. A059956, A065473, A256392.

Programs

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]]

PARI

prodeulerrat((1 - 1/p)^3 * (1 + 3/p)) \\ Amiram Eldar, Jun 29 2023

Formula

Equals Product_{p prime} (1 - 1/p)^3 * (1 + 3/p).