Problem 884

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?

Source: erdosproblems.com/884

Number theory
Divisors

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SolvedDisproved

An accepted solution exists. The statement is false.

DISPROVED (LEAN). The site's remarks credit a conditional disproof to Tao and an unconditional one to Larsen, and the Lean label rests on a third-party formalization of Larsen's proof; see Larsen's unconditional disproof; the conditional result is its own pending page, Tao's conditional disproof.

Problem 884

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