Möbius-$\mathcal{B}$-free topological entropy question

Let $\mathcal{B}$ be the defining set of the $\mathcal{B}$-free system, and let $X_{\mathcal{B},3}$ denote the Möbius-$\mathcal{B}$-free dynamical system with shift map $S$. Möbius-$\mathcal{B}$-free entropy question. Is the topological entropy equal to

$$h_{\mathcal{B},\mathrm{top}}(S,X_{\mathcal{B},3})=\prod_{b\in\mathcal{B}}\left(1-\frac{1}{b}\right)\log(3)?$$

The source explicitly presents this as a question rather than an assertion, and the supplied text does not resolve it.