Problem 859

Erdős Problem #859: declared status 'open'. Formalized: yes. 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 $t\to \infty$? Prize: no. Tags: divisors, number theory.