A335762 Decimal expansion of Product_{p prime} (1 + p/((p-1)*(p+1)^2)).

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

Offset

1,2

Comments

The asymptotic mean of A367987. - Amiram Eldar, Dec 23 2023

Links

Table of n, a(n) for n=1..105.

Formula

Equals Sum_{k>=1} 1/A000082(k) = Sum_{k>=1} 1/(k * A001615(k)).

Equals A013661 * A065465. - Amiram Eldar, Dec 23 2023

Example

1.450032145362120831608395887189223422325062117447167...

Mathematica

$MaxExtraPrecision = 1000; m = 1000; c = LinearRecurrence[{-1, 1, 2, 0, -1}, {0, 2, -3, 6, -5}, m]; RealDigits[Exp[NSum[Indexed[c, n]*(PrimeZetaP[n])/n, {n, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 100][[1]]

Prog

(PARI) prodeulerrat(1 + p/((p-1)*(p+1)^2)) \\ Amiram Eldar, Mar 18 2021

Crossrefs

Cf. A000082, A001615, A013661, A065465, A065484, A367987.

Sequence in context: A024247 A067445 A167003 * A254294 A143574 A262400

Adjacent sequences: A335759 A335760 A335761 * A335763 A335764 A335765

Keyword

nonn,cons

Author

Amiram Eldar, Jun 21 2020

Extensions

More digits from Vaclav Kotesovec, Sep 19 2020

Status

approved