Problem 884

Erdős Problem #884: declared status 'disproved'. Formalized: yes. Is it true that, for any $n$, if $d_1<\cdots <d_t$ are the divisors of $n$, then$$\sum_{1\leq i<j\leq t}\frac{1}{d_j-d_i} \ll 1+\sum_{1\leq i<t}\frac{1}{d_{i+1}-d_i},$$where the implied constant is absolute? Prize: no. Tags: divisors, number theory.