Problem

Source: 2021 Czech and Slovak Olympiad III A p4

Tags: number theory, divisor, divides



Find all natural numbers $n$ for which equality holds $n + d (n) + d (d (n)) +... = 2021$, where $d (0) = d (1) = 0$ and for $k> 1$, $ d (k)$ is the superdivisor of the number $k$ (i.e. its largest divisor of $d$ with property $d <k$). (Tomáš Bárta)