A382600 Decimal expansion of Sum_{p prime} 1/((p - 1)^3*p^3*(p + 1)^2).

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

Offset

0,3

Links

Table of n, a(n) for n=0..90.

Index to constants which are prime zeta sums {3,3,2}.

Formula

Equals -A085548 - A085541 + 39*A136141/16 - A086242 + A380840/4 - 9*A179119/16 + A382554/8.

Equals Sum_{k>=4} ((k-3)*(k-2)/2)*(P(2*k) + P(2*k+1)), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

Example

0.0141819306553361533538096655686...

Prog

(PARI) sumeulerrat(1/((p-1)^3*p^3*(p+1)^2)) \\ Amiram Eldar, Apr 01 2025

Crossrefs

Cf. A085541, A085548, A086242, A136141, A179119, A380840, A382554.

Sequence in context: A334451 A040019 A240776 * A394997 A019768 A319296

Adjacent sequences: A382597 A382598 A382599 * A382601 A382602 A382603

Keyword

nonn,cons

Author

Artur Jasinski, Mar 31 2025

Status

approved