All positive divisors of a positive integer are written on a blackboard. Two players and play the following game taking alternate moves. In the firt move, the player erases . If the last erased number is , then the next player erases either a divisor of or a multiple of . The player who cannot make a move loses. Determine all numbers for which can win independently of the moves of .
|2048||IMO Shortlist 2000 problem C4||3|
|2074||IMO Shortlist 2001 problem C4||8|
|2102||IMO Shortlist 2002 problem C4||1|
|2243||IMO Shortlist 2007 problem C3||5|
|2259||IMO Shortlist 2007 problem N3||6|
|2440||MEMO 2010 ekipno problem 3||2|