Let $2\leq d_1 < d_2,...,d_l < n$ be all the proper nontrivial divisors of $n$. I like to understand how much these divisors deviates from each other. Here are two questions in this regard:

(1) What is the maximum of the set $\{d_i/d_{i-1}: 1\leq i \leq l\}$. Say it $M$.

Assume that you know the prime factorization of $n (= p_1^{\alpha_1}..p_r^{\alpha_r})$. Can I have a formula in terms of $p_i$'s and $\alpha_i$'s. One of the crude upper bound can be $p_r$ but this is really bad if $n$ has many distinct prime factors.

(2) Instead of maximum, the average may be more interesting and useful. So can we estimate the mean and variance,

$\mu = (1/l)\sum_{i=1}^{l}{d_i/d_{i-1}}$ and $\sigma^2 = (1/l)\sum_{i=1}^{l}{(d_i/d_{i-1}-\mu)^2}$