Does any of you know if the inequality

$\displaystyle \frac{\phi(\sigma(n))}{n} < (\log \log \log n)^{-1/2}$

is true for all $n$ sufficiently large?

I remember reading something to that effect sometime ago, but a detailed statement of the result eludes me now and that's the reason that you find me asking it here.

I thank you all for your replies.