Square-free integer

A square-free integer is a number which is not divisible by any square numbers other than 1. In other words, each prime number that appears in its prime factorization appears exactly once.

For example, ${\displaystyle 6=2\times 3}$ is square-free. However, ${\displaystyle 27=3^{3}}$ is not square-free: it is divisible by ${\displaystyle 9=3^{2}}$, and the power of ${\displaystyle 3}$ in the prime factorization is to a power larger than one.