Problem

Source: Iran MO Third Round N3

Tags: number theory



We call natural number $m$ ziba, iff every natural number $n$ with the condition $1\le n\le m$ can be shown as sum of [some of] positive and distinct divisors of $m$. Prove that infinitely ziba numbers in the form of $(k\in\mathbb{N})k^2+k+2022$ exist.