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%I #10 Mar 17 2021 03:25:14
%S 8,4,5,4,3,7,3,1,3,9,8,6,6,8,5,4,6,9,9,6,0,3,6,2,7,3,7,5,6,8,0,3,7,8,
%T 9,3,8,0,4,6,7,2,6,3,3,1,2,8,0,6,9,6,0,4,3,6,1,8,4,9,6,9,5,4,2,7,5,8,
%U 5,0,8,8,5,3,2,8,1,3,5,4,9,3,8,4,5,9,1,1,9,5,7,7,4,1,3,3,6,1,4,5,7,1,3,5,1,8
%N Decimal expansion of Product_{p prime} (1 - 7/p^3).
%C This is the probability that k, k+1, ... k+6 all are cubefree, or equivalently, the asymptotic density of A328016.
%H Leon Mirsky, <a href="https://doi.org/10.1112/plms/s2-50.7.497">Arithmetical pattern problems relating to divisibility by rth powers</a>, Proceedings of the London Mathematical Society, Vol. s2-50, No. 1 (1949), pp. 497-508.
%e 0.084543731398668546996036273756803789380467263312806...
%t $MaxExtraPrecision = 600; m = 600; c = LinearRecurrence[{0, 0, 7}, {0, 0, -7}, m]; RealDigits[(1/8) * Exp[3*NSum[Indexed[c, n]*(PrimeZetaP[n] - 1/2^n)/n, {n, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 100][[1]]
%o (PARI) prodeulerrat(1 - 7/p^3) \\ _Amiram Eldar_, Mar 17 2021
%Y Cf. A206256, A328016.
%K nonn,cons
%O -1,1
%A _Amiram Eldar_, Oct 01 2019
%E More terms from _Vaclav Kotesovec_, May 29 2020
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