For a natural number n, let $1 = d_1 < \dotsc < d_{\tau(n)} = n$ denote the divisors of n in increasing order. Does it hold that $\sum_{1 \le i < j \le \tau(n)} \frac{1}{d_j - d_i} \ll 1 + \sum_{1 \le i < \tau(n)} \frac{1}{d_{i + 1} - d_i}$ for $n \to \infty`$, i.e. Unparsed notation: \sum_{1 \le i < j \le \tau(n)} \frac{1}{d_j - d_i} \in O \left( 1 + \sum_{1 \le i < \tau(n)} \frac{1}{d_{i + 1} - d_i}) Unparsed notation: \right)?

In September 2025, Terence Tao gave a conditional _negative_ answer to Erdos conjecture 884, disproving it under the assumption of the *Qualitative Hardy-Littlewood Conjecture*. See here. The *qualitative* version of the conjecture only states that there are infinitely many tuples of primes and does not require any asymptotical bounds and as such is a corollary of the general form of the Hardy-Littlewood Conjecture. We state the 'weaker' implication using general Hardy-Littlewood here, since this conjecture is already formalized.