Definition:Square-Free Integer

Let $$n \in \Z$$.

Then $$n$$ is square-free iff $$n$$ has no divisor which is the square of a prime.

That is, iff the prime decomposition $$n = p_1^{k_1} p_2^{k_2} \ldots p_r^{k_r}$$ is such that $$\forall i: 1 \le i \le r: k_i = 1$$.