A065480 Decimal expansion of Product_{p prime} (1 - 1/(p^2+p-1)).

6, 6, 9, 5, 8, 0, 2, 9, 0, 5, 3, 9, 0, 6, 2, 3, 6, 7, 6, 3, 5, 0, 2, 5, 6, 9, 5, 6, 1, 2, 4, 3, 4, 2, 2, 7, 2, 1, 7, 3, 3, 9, 8, 2, 5, 4, 1, 6, 2, 3, 3, 0, 2, 5, 6, 2, 4, 6, 5, 4, 6, 2, 6, 3, 3, 0, 9, 8, 3, 6, 6, 1, 9, 9, 5, 4, 7, 2, 4, 5, 7, 1, 4, 5, 7, 5, 6, 6, 2, 6, 0, 3, 8, 6, 9, 6, 3, 8

Offset

0,1

Comments

The probability that two numbers are coprime given that they are both coprime to a randomly chosen third number. - Luke Palmer, Apr 27 2019

Links

Table of n, a(n) for n=0..97.

G. Niklasch, Some number theoretical constants: 1000-digit values. [Cached copy]

Formula

Equals A065473*zeta(2)/A065463. - Luke Palmer, Apr 27 2019

Example

0.6695802905390623676350256956124342...

Mathematica

digits = 98; Exp[NSum[(1/2)*(-2 + (-2)^n - ((1/2)*(-1 - Sqrt[5]))^n*(-1 + Sqrt[5]) + ((1/2)*(-1 + Sqrt[5]))^n*(1 + Sqrt[5]))*PrimeZetaP[n - 1]/(n - 1), {n, 3, Infinity}, WorkingPrecision -> 4 digits, Method -> "AlternatingSigns"]] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Apr 18 2016 *)

Prog

(PARI) prodeulerrat(1 - 1/(p^2+p-1)) \\ Amiram Eldar, Mar 14 2021

Crossrefs

Cf. A065592, A078081.

Cf. A013661, A065463, A065473.

Sequence in context: A217852 A021603 A250721 * A198116 A200023 A339705

Adjacent sequences: A065477 A065478 A065479 * A065481 A065482 A065483

Keyword

cons,nonn

Author

N. J. A. Sloane, Nov 19 2001

Status

approved