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A303494 Decimal expansion of Sum_{p prime} log(p)/p^4.

%I A303494 #12 Feb 16 2025 08:33:54
%S A303494 0,6,0,6,0,7,6,3,3,3,5,0,7,7,0,0,6,3,3,9,2,2,3,0,9,8,3,7,0,9,7,1,3,3,
%T A303494 7,8,4,0,6,3,8,2,8,7,7,4,6,1,2,5,9,8,4,3,9,9,1,1,2,7,6,8,1,7,3,4,1,5,
%U A303494 2,6,7,6,7,8,4,5,3,9,9,6,7,9,2,5,9,0,8,1,3,8,1,5,4,9,8,2,5,5,5,7,3
%N A303494 Decimal expansion of Sum_{p prime} log(p)/p^4.
%C A303494 The negated first derivative of the Prime Zeta function at 4.
%H A303494 R. J. Mathar, <a href="https://arxiv.org/abs/0803.0900">Series of reciprocal powers of k-almost primes</a>, arXiv:0803.0900 (2008) Table 3, s=4.
%H A303494 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 A303494 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/PrimeZetaFunction.html">Prime Zeta Function</a>
%H A303494 Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_zeta_function">Prime Zeta Function</a>
%e A303494 0.060607633350770063392230983709713378406382877461259843991127681734...
%t A303494 RealDigits[PrimeZetaP'[4], 10, 100][[1]]
%Y A303494 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 A303494 nonn,cons
%O A303494 0,2
%A A303494 _Jean-François Alcover_, Apr 25 2018