A330595 Decimal expansion of Product_{primes p} (1 + 1/p^2 + 1/p^3).

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

Offset: 1

Author

Vaclav Kotesovec, Dec 19 2019

Keywords

• nonn
• cons

Examples

			1.748932997843245303033906997685114802259883493595480897273662144084849...
		

Crossrefs

Cf. A065464, A065473, A065476, A160889, A328017, A330594, A330596, A338325.

Programs

Mathematica

Do[Print[N[Exp[-Sum[q = Expand[(-p^2 - p^3)^j]; Sum[PrimeZetaP[Exponent[q[[k]], p]] * Coefficient[q[[k]], p^Exponent[q[[k]], p]], {k, 1, Length[q]}]/j, {j, 1, t}]], 110]], {t, 20, 200, 20}]

PARI

prodeulerrat(1 + 1/p^2 + 1/p^3) \\ Vaclav Kotesovec, Sep 19 2020

Formula

Equals Sum_{n>=1} 1/A338325(n). - Amiram Eldar, Oct 26 2020