Divisor game

Let $N \ge 2$ be a positive integer. Alice and Bob play the following divisor game: starting with the set $D_N$ of positive divisors of $N$, the players take turns removing some elements from the set. At a player's turn, he or she chooses a divisor $d$ that remains, and removes $d$ and any of the divisors of $d$ that remain. The player who moves last loses.

For example: $N = 18, D_N = \{ 1,2,3,6,9,18 \}$. Alice chooses $d=2$, so she removes $1$ and $2$. The remaining set is $\{3,6,9,18\}$. Bob chooses $d = 9$ and so must also remove $3$. The remaining set is $\{6,18\}$. Alice takes $6$, and now Bob is forced to take $18$, so he loses.

Let $n \ge 2$ be the largest positive integer $\le 200$ such that if Alice and Bob play the divisor game for $n$ and both of them play optimally, the second player wins. Find $n$. If no such $n$ exists, enter $999$.