A373809 Decimal expansion of the second derivative P''(2) of the prime zeta function at 2.

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

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Tengiz O. Gogoberidze, Baker's dozen digits of two sums involving reciprocal products of an integer and its greatest prime factor, arXiv:2407.12047 [math.GM], 2024, Table 2, s=2.

Formula

Equals Sum_{primes = 2,3,5,7,...} log(p)^2/p^2.

Example

0.74159785498280500302394032754503754132161405686935...

Mathematica

$MaxExtraPrecision = 200; RealDigits[N[PrimeZetaP''[2], 120]][[1]] (* Amiram Eldar, Aug 19 2024 *)

Crossrefs

Cf. A085548 (P(2)), A136271 (P'(2)).

Sequence in context: A376845 A328416 A372275 * A010508 A070403 A144468

Adjacent sequences: A373806 A373807 A373808 * A373810 A373811 A373812

Keyword

nonn,cons

Author

R. J. Mathar, Aug 18 2024

Extensions

More terms from Amiram Eldar, Aug 19 2024

Status

approved