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%I #35 Aug 20 2020 08:31:56
%S 8,3,1,9,0,7,3,7,2,5,8,0,7,0,7,4,6,8,6,8,3,1,2,6,2,7,8,8,2,1,5,3,0,7,
%T 3,4,4,1,7,0,5,6,3,9,7,7,3,3,7,2,8,0,7,9,2,7,9,6,7,0,3,3,2,8,6,4,4,5,
%U 7,8,7,9,1,7,2,3,4,7,9,8,8,8,2,1,3,6,5,6,6,8,9,8,9,9,6,5,3,0,4,0,9,8
%N Decimal expansion of 1/zeta(3).
%C This is the probability that three randomly chosen integers are relatively prime (see A018805). - Gary McGuire, Dec 13 2004
%C This is also the probability that a random integer is cubefree. - Eugene Salamin, Dec 13 2004
%C On the other hand, the probability that three randomly-chosen integers are pairwise relatively prime is given by A065473. - _Charles R Greathouse IV_, Nov 14 2011
%C This is also the 'probability' that a random algebraic number's denominator is equal to its leading coefficient, see Arno, Robinson, & Wheeler. - _Charles R Greathouse IV_, Nov 12 2014
%C This is the probability that a random point on a cubic lattice is visible from the origin, i.e., there is no other lattice point that lies on the line segment between this point and the origin. - _Amiram Eldar_, Jul 08 2020
%H Steven Arno, M. L. Robinson, and Ferell S. Wheeler, <a href="https://doi.org/10.1006/jnth.1996.0049">On denominators of algebraic numbers and integer polynomials</a>, Journal of Number Theory 57:2 (April 1996), pp. 292-302.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RelativelyPrime.html">Relatively Prime</a>
%F From _Amiram Eldar_, Aug 20 2020: (Start)
%F Equals Sum_{k>=1} mu(k)/k^3, where mu is the Möbius function (A008683).
%F Equals Product_{p prime} (1 - 1/p^3). (End)
%e 0.831907372580707468683126278821530734417...
%t RealDigits[1/Zeta[3],10,120][[1]] (* _Harvey P. Dale_, May 31 2019 *)
%o (Maxima) fpprec : 200$ bfloat( 1/zeta(3))$ bfloat(%); /* _Martin Ettl_, Oct 15 2012 */
%o (PARI) 1/zeta(3) \\ _Charles R Greathouse IV_, Nov 12 2014
%Y Cf. A002117, A008683.
%K nonn,cons,easy
%O 0,1
%A _Eric W. Weisstein_, Sep 30 2003
%E Entry revised by _N. J. A. Sloane_, Dec 16 2004
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