For a set $\mathcal{B} \subset \mathbb{N} \setminus \{1\}$, let $\mathcal{B}$-free integers be the set of integers that are not divisible by any element of $\mathcal{B}$ and let $X^{\mathcal{B}} \subset \{0,1\}^{\mathbb{Z}}$ be the closure of the orbit of the indicator of $\mathcal{B}$--free integers under the left shift $T$.  One can equip $\left(X^{\mathcal{B}},T\right)$ with the $T$--invariant measure which produces the correlations of $\mathcal{B}$-free integers. For an infinite, coprime $\mathcal{B}$ with $\sum_{b \in \mathcal{B}} 1/b