OPEN

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?

#884: [Er98]

number theory, divisors