Improved Bounds for Distinct Multiples in Intervals

Kaizhe Chen, Samuel Korsky

For $n\ge 1$, let $F(n)$ be the least $H$ such that any $H$ consecutive integers contain $n$ pairwise distinct integers $a_1,a_2,\dots ,a_n$ with $k\mid a_k$ for $1\le k\le n$, a…