Let be a positive integer. Alice and Bob play the following divisor game: starting with the set of positive divisors of , the players take turns removing some elements from the set. At a player's turn, he or she chooses a divisor that remains, and removes and any of the divisors of that remain. The player who moves last loses.
For example: . Alice chooses , so she removes and . The remaining set is . Bob chooses and so must also remove . The remaining set is . Alice takes , and now Bob is forced to take , so he loses.
Let be the largest positive integer such that if Alice and Bob play the divisor game for and both of them play optimally, the second player wins. Find . If no such exists, enter .