A382569 Decimal expansion of Sum_{p prime} 1/(p^3*(p + 1)^2).

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

Offset

0,3

Links

Table of n, a(n) for n=0..103.

Index to constants which are prime zeta sums {3,0,2}.

Formula

Equals -2*A085548 + A085541 + 3*A179119 - A382554.

Equals Sum_{k>=5} (-1)^(k+1) * (k-4) * P(k), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

Example

0.016480273853328955503361977914094146924354041689814015912823807...

Prog

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

Crossrefs

Cf. A085541, A085548, A179119, A382554.

Sequence in context: A118289 A075495 A070652 * A195487 A073746 A010496

Adjacent sequences: A382566 A382567 A382568 * A382570 A382571 A382572

Keyword

nonn,cons

Author

Artur Jasinski, Mar 31 2025

Status

approved