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 ? When I say "distinct" prime powers, it means the base has got to be different.

After some experimentation I find that if is the random number, then has on average 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 :)