Let $S$ be a set of positive integers, for example $S$ could consist of 3, 4, and 8.

A positive integer $n$ is called an $S$-number if and only if for every factor $m$ of $n$ with $m>1$, the number $m$ is a multiple of some number in $S$.

So in the above example, 9 is an $S$-number; this is because the factors of 9 greater than 1 are 3 and 9, and each of these is a multiple of 3.

Positive integer $n$ is therefore not an $S$-number if and only if