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In this note, we prove that there is no transcendental entire function $f\left(z\right)\in \mathbb{Q}\left[\right[z\left]\right]$ such that $f\left(\mathbb{Q}\right)\subseteq \mathbb{Q}$ and $\mathrm{den}f(p/q)=F\left(q\right)$, for all sufficiently large $q$, where $F\left(z\right)\in \mathbb{Z}\left[z\right]$.