A256392 Decimal expansion of Product_{p prime} (1-4/p^2+4/p^3-1/p^4).

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

Offset

0,1

Comments

Also decimal expansion of the probability that an integer tuple (x,y,z,w) satisfies gcd(x,y) = gcd(y,z) = gcd(z,w) = gcd(w,x) = 1.

Links

Juan Arias-de-Reyna, Table of n, a(n) for n = 0..1000

Juan Arias de Reyna and Randell Heyman, Counting Tuples Restricted by Pairwise Coprimality Conditions, J. Int. Seq., Vol. 18 (2015), Article 15.10.4; arXiv preprint, arXiv:1403.2769 [math.NT], 2014.

Example

0.2177787166195363783230075141...

Mathematica

Do[Print[N[Exp[-Sum[q = Expand[(4 p^2 - 4 p^3 + p^4)^j]; Sum[PrimeZetaP[Exponent[q[[k]], p]] * Coefficient[q[[k]], p^Exponent[q[[k]], p]], {k, 1, Length[q]}]/j, {j, 1, t}]], 50]], {t, 10, 100, 10}] (* Vaclav Kotesovec, Dec 17 2019 *)

Prog

(PARI) prodeulerrat(1-4/p^2+4/p^3-1/p^4) \\ Amiram Eldar, Mar 03 2021

Crossrefs

Cf. A065473, A196524, A256391, A330523, A336643.

Sequence in context: A217106 A329995 A086054 * A011134 A157240 A144749

Adjacent sequences: A256389 A256390 A256391 * A256393 A256394 A256395

Keyword

nonn,cons

Author

Juan Arias-de-Reyna, Mar 28 2015

Status

approved