MEMO 2010 pojedinačno problem 2

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April 28, 2012
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.
Source: Srednjoeuropska matematička olimpijada 2010, pojedinačno natjecanje, problem 2