Erdős Problem #859 — Let $t\geq 1$ and let $d_t$ be the density of the set of integers $n\in\mathbb{N}$ for which $t$ can be represented as the sum of distinct divisors of $n$.

Let $t\geq 1$ and let $d_t$ be the density of the set of integers $n\in\mathbb{N}$ for which $t$ can be represented as the sum of distinct divisors of $n$. Do there exist constants $c_1,c_2>0$ such that $d_t \sim \frac{c_1}{(\log t)^{c_2}}$ as $t\to \infty$?