How many distinct prime powers divide n ?

Hello,

I'm looking for an empirical result (if it can be proved it is better but not required) that could tell me how many *distinct* prime powers would divide a randomly chosen $\displaystyle n$ ? When I say "distinct" prime powers, it means the base has got to be different.

After some experimentation I find that if $\displaystyle n$ is the random number, then $\displaystyle n$ has on average $\displaystyle \ln{(\log{(n)})}$ distinct prime powers, but before I attempt a large scale data collection I was just wondering if you guys knew any results that could save me two days of intense computing ?

Thanks all :)