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A303493 Decimal expansion of Sum_{p prime} log(p)/p^3.

%I A303493 #15 Feb 16 2025 08:33:54
%S A303493 1,5,0,7,5,7,5,5,5,5,4,3,9,5,0,4,2,2,1,7,9,8,3,6,5,1,6,3,6,5,3,4,2,9,
%T A303493 1,9,5,7,5,5,0,1,1,6,1,5,3,0,6,8,9,3,3,1,8,1,8,7,9,7,6,7,6,0,4,2,5,5,
%U A303493 8,4,1,8,4,2,7,0,9,7,1,7,7,6,2,2,8,8,8,8,8,0,8,4,8,3,6,3,6,5,7,7
%N A303493 Decimal expansion of Sum_{p prime} log(p)/p^3.
%C A303493 The negated first derivative of the Prime Zeta function at 3.
%H A303493 R. Mathar, <a href="https://arxiv.org/abs/0803.0900">Series of reciprocal powers of k-almost primes</a>, arXiv:0803.0900 [math.NT], 2008-2009; Table 3, s=3.
%H A303493 J. B. Rosser, L. Schoenfeld, <a href="https://projecteuclid.org/euclid.ijm/1255631807">Approximate formulas for some functions of prime numbers</a>, Ill. J. Math. 6 (1) (1962) 64-94, Table IV
%H A303493 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/PrimeZetaFunction.html">Prime Zeta Function</a>
%H A303493 Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_zeta_function">Prime Zeta Function</a>
%e A303493 0.150757555543950422179836516365342919575501161530689331818797676...
%t A303493 RealDigits[PrimeZetaP'[3], 10, 100][[1]]
%Y A303493 Decimal expansion of Sum_{p prime} log(p)/p^k: A136271 (k=2), A303493 (k=3), A303494 (k=4), A303495 (k=5), A303496 (k=6), A303497 (k=7), A303498 (k=8), A303499 (k=9).
%K A303493 nonn,cons
%O A303493 0,2
%A A303493 _Jean-François Alcover_, Apr 25 2018