Given $\alpha\in\Bbb N$, can there be more than $(\log N)^4$ divisors (composites allowed) of $N$ in $\big[\frac\alpha2,\alpha\big]$ when $\sqrt N\in\big[\frac\alpha2,\alpha\big]$?
What is the maximum number of divisors asymptotically?
4 of 5
added 58 characters in body
On the number of divisors in a given range
user76479