A330523 Decimal expansion of Product_{primes p} (1 - 1/p^2 - 1/p^3 + 1/p^4).

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

Offset

0,1

Links

Table of n, a(n) for n=0..105.

Formula

Equals (6/Pi^2) * A065465. - Amiram Eldar, Sep 08 2020

Example

0.5358961538283379998085026313185459506482223745141452711510108346133288119...

Mathematica

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

Prog

(PARI) (6/Pi^2) * prodeulerrat(1 - 1/(p^2*(p+1))) \\ Amiram Eldar, Sep 08 2020

Crossrefs

Cf. A055653, A062354, A065465, A175639, A256392, A332713.

Sequence in context: A128010 A185046 A114740 * A361546 A128008 A265800

Adjacent sequences: A330520 A330521 A330522 * A330524 A330525 A330526

Keyword

nonn,cons

Author

Vaclav Kotesovec, Dec 17 2019

Status

approved