Let $m,n\in \mathbb{Z}$, what is the notation usually used to say that $m,n$ have the same prime factors, i.e. $m=p_1^{m_1}p_2^{m_2}\cdots p_2^{m_r}$, $n=p_1^{n_1}p_2^{n_2}\cdots p_r^{n_r}$ for some primes $p_1,p_2\cdots,p_r$.
I think about Radical(n)=Radical(m), but maybe there is a better notation?
Bests.
The radical operator may suit your need. If $m$ is an integer such that $m = \Pi_{1}^{r}p_{j}^{m_j}$ for some integer $r > 0$ and some integers $m_{1}, \dots, m_{r} \geq 0$ and some primes $p_{1}, \dots, p_{r}$, the radical of $m$ is defined to be $\Pi_{1}^{r}p_{j}$ and is denoted by $rad(m)$. Then two integers $m, n$ have the same prime divisors if and only if $$rad(m) = rad(n).$$