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%I #5 May 11 2023 01:44:02
%S 5,8,7,2,6,1,8,8,2,0,8,1,3,8,4,2,3,9,1,0,7,4,1,3,8,1,4,2,6,6,7,8,3,5,
%T 6,1,1,4,8,6,2,6,4,3,1,1,0,8,2,9,3,5,3,5,1,7,0,7,9,8,0,4,6,6,9,0,3,9,
%U 8,2,0,5,3,5,0,1,1,2,5,3,5,6,8,6,3,3,7,5,7,9,1,7,5,1,3,0,1,2,1,3,1,6,8,4,3
%N Decimal expansion of zeta(3/4) * Product_{p prime} (1 + 1/p^(5/4) - 1/p^2 - 1/p^(9/4)) (negated).
%C The coefficient c_1 of the second term in the asymptotic formula for the number of cubefull numbers (A036966) not exceeding x, N(x) = c_0 * x^(1/3) + c_1 * x^(1/4) + c_2 * x^(1/5) + o(x^(1/8)) (Bateman and Grosswald, 1958; Finch, 2003).
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, section 2.6.1, pp. 113-115.
%H Paul T. Bateman and Emil Grosswald, <a href="https://doi.org/10.1215/ijm/1255380836">On a theorem of Erdős and Szekeres</a>, Illinois Journal of Mathematics, Vol. 2, No. 1 (1958), pp. 88-98.
%H P. Shiu, <a href="https://doi.org/10.1017/S0017089500008351">The distribution of cube-full numbers</a>, Glasgow Mathematical Journal, Vol. 33, No. 3 (1991), pp. 287-295.
%H P. Shiu, <a href="https://doi.org/10.1017/S0305004100070705">Cube-full numbers in short intervals</a>, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 112, No. 1 (1992), pp. 1-5.
%e -5.87261882081384239107413814266783561148626431108293...
%o (PARI) zeta(3/4) * prodeulerrat(1 + 1/p^5 - 1/p^8 - 1/p^9 ,1/4)
%Y Cf. A036966, A090699, A244000, A362973, A362974 (c_0), A362976 (c_2).
%K nonn,cons
%O 1,1
%A _Amiram Eldar_, May 11 2023
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