A330596 Decimal expansion of Product_{primes p} (1 - 1/p^2 + 1/p^3).

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

Offset: 0

Author

Vaclav Kotesovec, Dec 19 2019

Keywords

• nonn
• cons

Comments

The asymptotic density of A337050. - Amiram Eldar, Aug 13 2020

Examples

			0.748535259682363564644215048637910601641640343005324404515852793925925...
		

Crossrefs

Cf. A057723, A065464, A065473, A065476, A065487, A328017, A330594, A330595, A337050, A372636.

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) \\ Amiram Eldar, Mar 17 2021

Formula

Equals (6/Pi^2) * A065487. - Amiram Eldar, Jun 10 2020