|
|
A088453
|
|
Decimal expansion of 1/zeta(3).
|
|
23
|
|
|
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, 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, 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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
This is the probability that three randomly chosen integers are relatively prime (see A018805). - Gary McGuire, Dec 13 2004
This is also the probability that a random integer is cubefree. - Eugene Salamin, Dec 13 2004
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
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
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
|
|
LINKS
|
|
|
FORMULA
|
Equals Sum_{k>=1} mu(k)/k^3, where mu is the Möbius function (A008683).
Equals Product_{p prime} (1 - 1/p^3). (End)
|
|
EXAMPLE
|
0.831907372580707468683126278821530734417...
|
|
MATHEMATICA
|
|
|
PROG
|
(Maxima) fpprec : 200$ bfloat( 1/zeta(3))$ bfloat(%); /* Martin Ettl, Oct 15 2012 */
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|