All Questions

According to Hardy-Ramanujan/Erdős-Kac we know that usually there are $\sim\log\log n$ prime numbers in a factorization. But if you pick up a natural number at random, and you factor it, what is the ...

If $x \ge y \ge 1$ are real numbers and if $k$ is a positive integer, take $\Phi_k(x, y)$ to be the number of integers $\le x$ with exactly $k$ prime factors and no prime factor $\le y$. If $y$ is ...

I've tagged this as reference request as surely this question must be very well investigated, I just don't know how to look for it. Most likely the perfect answer will be in form of a keyword for ...