Question 125
There are $n$ candies on the table. On every turn, a player eats a number of candies that is greater than $1$ and divides the number of candies on the table at the start of the turn, but must leave at least $1$ candy on the table. Two players take alternate turns and the player who is unable to make a move loses. Find all positive integers $n$ for which the first player can always win.