This is my first question.
Let $a_1, a_2,\ldots, a_k$ be natural numbers $\leq n$ with $m$ prime factors.
Let $p_1, p_2, \ldots, p_r$ be the prime numbers $\leq n$.
Let $C_{m,n} = \frac{\sum_{i=1}^{k}a_i}{\sum_{i=1}^{r}p_i}$ Does the following limit exist when $m\geq 2$? Obviously, when $m=1$, $C_{1,n}=1$.
$\lim_{n\to \infty} C_{m,n}$
I have some guesses but not defendable enough.
My best,
The FM.