A340153 - OEIS

%I #8 Feb 13 2021 16:26:31

%S 6,7,6,8,9,2,7,3,7,0,0,9,8,8,1,9,9,3,6,1,0,2,3,7,3,2,6,7,2,4,3,8,9,2,

%T 1,2,7,9,7,6,7,8,3,9,7,4,5,9,7,8,8,8,4,5,2,7,3,2,9,7,8,2,3,0,4,4,3,2,

%U 6,3,2,0,4,6,0,3,5,7,8,6,0,5,1,2,8,3,2,6,8,4,8,1,1,1,1,0,8,4,4,9,3,1,7,0,8,4

%N Decimal expansion of Product_{p prime} (1 - 2/p^3).

%C The asymptotic density of the sequence of cubefree numbers k such that k+1 is also cubefree (A340152) (Carlitz, 1932).

%H Leonard Carlitz, <a href="https://doi.org/10.1093/qmath/os-3.1.273">On a problem in additive arithmetic (II)</a>, The Quarterly Journal of Mathematics, Vol. os-3, No. 1 (1932), pp. 273-290.

%e 0.67689273700988199361023732672438921279767839745978...

%t $MaxExtraPrecision = 500; m = 500; c = LinearRecurrence[{0, 0, 2}, {0, 0, -6}, m]; RealDigits[Exp[NSum[Indexed[c, n]*(PrimeZetaP[n])/n, {n, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 100][[1]]

%o (PARI) prodeulerrat(1 - 2/p^3)

%Y Cf. A065474, A340152.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Dec 29 2020

%E More digits from _Vaclav Kotesovec_, Jan 16 2021