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

.

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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 $B$.