MathNet 2017-part-02 — 176 problems (EN–VI) Question 95

Define $a_1 = 1$, and for each $n \gt 1$ let $a_n = n \cdot a_{\lfloor \frac{n}{2} \rfloor}$. Prove that for each $n \ge 12$ we have $a_n \gt n^2$.