In defining perfect numbers we want that the sum of its divisors (including itself) is equal twice the number itself. We can define more general classes of numbers such that sum of its divisors is divisible by the number itself, i.e. we can ask is it true that for every $k \in \mathbb N (k>1)$ there exists at least one (or infinitely many) natural numbers such that the sum of their divisors is equal to $kn$.
But what happens if we sum non-divisors?
As an example let us take the number $12$. It is divisible by $1,2,3,4,6,12$ so the sum of its non-divisors is $5+7+8+9+10+11=50$ and $50$ is not a multiple of $12$.
What is the smallest number $n>2$ such that the sum of its non-divisors is a multiple of $n$?
(if you find more than one number of this kind feel free to post it in an answer)