# Mean of highest exponent in prime factorization of all integers ≥ 2

For any natural number $n > 1$, define $E(n)$,to be the highest exponent to which a prime divides it. For instance, $E(12)=E(36)=2$. Show that $$\lim_{N \to \infty} \frac{1}{N} \sum\limits_{n=2}^{N} E(n)$$ exists and find its value

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Can you give a title that is more specific next time you ask a question? The title is used for searching so it's important be precise. – kennytm Aug 11 '10 at 9:47
@Kenny TM: hi, i can only give the title which comes to my mind at that time. In case you don't like it then please be free to edit it. Sorry – anonymous Aug 11 '10 at 14:39
That sounds very sloppy. Coming up with a useful title is one of the few tokens of respect you can give to would-be answerers. – J. M. Aug 11 '10 at 14:46
@J.Mangaldan:- I agree. – anonymous Aug 11 '10 at 15:27
As with all your questions: (1) where is this question from, (2) why you want to know? If you provide more personal context and motivation, I suspect more people will feel like trying/answering. – ShreevatsaR Aug 11 '10 at 15:45