Kovač and Tao [KoTa24] generally proved that any strictly increasing sequence of positive integers $a_n$ such that $\sum \frac{1}{a_n}$ converges and $$\liminf_{n \to \infty} (a_n^2 \sum_{k > n} \frac{1}{a_k^2}) > 0$$ is not an irrationality sequence.