For any positive integer $n$ let $s(n)$ be the sum of its digits in decimal representation. Find all numbers $n$ for which $s(n)$ is the largest proper divisor of $n$.
Source: 2006 Romania JBMO TST 1.3
Tags: sum of digits, number theory, divisor
For any positive integer $n$ let $s(n)$ be the sum of its digits in decimal representation. Find all numbers $n$ for which $s(n)$ is the largest proper divisor of $n$.