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All positive divisors of a positive integer

N

are written on a blackboard. Two players

A

and

B

play the following game taking alternate moves. In the firt move, the player

A

erases

N

. If the last erased number is

d

, then the next player erases either a divisor of

d

or a multiple of

d

. The player who cannot make a move loses. Determine all numbers

N

for which

A

can win independently of the moves of

B

.
(4th Middle European Mathematical Olympiad, Individual Competition, Problem 2)

Problem Statement