A375509 Decimal expansion of the negated derivative P'(3/2) of the prime zeta function at 3/2.
1, 2, 9, 5, 7, 1, 0, 7, 5, 4, 7, 9, 1, 6, 0, 7, 5, 5, 3, 7, 2, 2, 8, 8, 8, 3, 2, 4, 6, 4, 5, 5, 5, 7, 6, 6, 3, 4, 9, 4, 1, 6, 2, 9, 4, 6, 9, 8, 4, 5, 2, 9, 7, 5, 4, 4, 9, 6, 5, 1, 9, 7, 3, 8, 0, 1, 8, 1, 4, 4, 0, 0, 5, 2, 6, 6, 8, 1, 1, 7, 5, 7, 4, 3, 9, 6, 5, 1, 3, 4, 8, 7, 5, 5, 0, 0, 4, 4, 1, 1
Offset: 1
Examples
1.29571075479160755372288832464555766349416294698452...
Programs
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Mathematica
$MaxExtraPrecision = 100; RealDigits[N[PrimeZetaP'[3/2], 120]][[1]] (* Amiram Eldar, Aug 19 2024 *)
Formula
P'(3/2) = -Sum_{p = 2,3,5,7,11,..} log(p)/p^(3/2) = -1.29571075479160755372...