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

%I #13 Mar 16 2021 04:06:49

%S 1,1,0,6,9,6,0,1,1,1,9,5,3,2,1,7,6,7,6,6,5,1,1,7,9,1,3,0,0,0,7,4,3,9,

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

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

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

%e 1.106960111953217676651179130007439592949548833658122419043134044978777...

%t Do[Print[N[Exp[-Sum[q = Expand[(-p^2 + 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}]

%o (PARI) prodeulerrat(1 + 1/p^2 - 2/p^3) \\ _Amiram Eldar_, Mar 16 2021

%Y Cf. A065464, A065473, A065476, A208133, A328017, A330595, A330596.

%K nonn,cons

%O 1,4

%A _Vaclav Kotesovec_, Dec 19 2019