Typo on A002117

[Gerald McGarvey]

Some web pages with complete proofs (or sketches of proofs)
of the probability of two random numbers being coprime:

Probability of Random Numbers Being Coprime:
http://mathforum.org/library/drmath/view/55801.html

Probability of two numbers being Coprime:
http://www.ballandclaw.com/upi/coprime.html

Riemann zeta function:
http://en.wikipedia.org/wiki/Riemann_zeta_function

The MathWorld web page 'Relatively Prime' gives two references
http://mathworld.wolfram.com/RelativelyPrime.html
and also provides information on a generalization to n random integers.

Finch in 'Mathematical Constants' gives these two references:
Hardy and Wright 'An Introduction to the Theory of Numbers' pp. 47,268-269
Yaglom and Yagom 'Challenging Mathematical Problems with Elementary 
Solutions' ex. 92-93

- Gerald

At 10:44 PM 12/8/2005, Tautócrona wrote:
>On A002117, the decimal expansion of zeta(3), it is said in the comments:
>
>"[...] In Chapter 8 we pointed out that the probability that two random 
>integers are
>relatively prime is Pi^2/6, which is Zeta(2). This generalizes to: The 
>probability that k
>random integers are relatively prime is Zeta(k) "
>
>Pi^2 / 6 can't be a probability, since it's bigger than 1. I know the real 
>probability is
>its inverse, 6 / pi^2 (as proved by Dirichlet) and therefore I suspect 
>that the
>generalization is with Zeta(k)^(-1) (assuming the first term of the series 
>is 1).
>
>As this comment seems to be extracted from a book, if it's well extracted, 
>then we may
>contact the author and let him know.
>
>By the way, anyone knows where to find the complete proof for this result?
>
>Jose Brox