Question 2
David and Linus play the following game: David chooses a subset $Q$ of the set $\{1, \ldots, 2018\}$. Then Linus chooses a natural number $a_{1}$ and computes the numbers $a_{2}, \ldots, a_{2018}$ recursively, where $a_{n+1}$ is the product of the positive divisors of $a_{n}$.
Let $P$ be the set of natural numbers $k \in\{1, \ldots, 2018\}$ for which $a_{k}$ is a perfect square. Linus wins if $P=Q$. Otherwise David wins. Who has a winning strategy?
Let $P$ be the set of natural numbers $k \in\{1, \ldots, 2018\}$ for which $a_{k}$ is a perfect square. Linus wins if $P=Q$. Otherwise David wins. Who has a winning strategy?