Typo on A002117

[Tautócrona]

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