Erdős–Rosenfeld conjecture on divisors near the square root

Let $n$ be a positive integer, and let $c$ be a real number. Consider the divisors of $n$ in the interval

$$\sqrt{n}-c\sqrt[4]{n}\leq d\leq \sqrt{n}+c\sqrt[4]{n}.$$

Erdős–Rosenfeld conjecture. There is an absolute constant $K$ such that, for every $c$, the number of such divisors is at most $K$ whenever $n>n_0(c)$.

The conjecture asks whether every positive integer has only boundedly many divisors in a short interval around its square root. The source reports results for perfect squares and almost squares, but does not state that the conjecture is resolved in general.