10: Amnesty (part 1)

The cells in a jail are numbered consecutively. As part of an amnesty, the jailer unlocks all the cells. Next, he locks every even numbered cell. Then he turns the key in every cell divisible by 3, locking unlocked cells and unlocking locked cells. He continues in this way, on his nth trip turning the key in every cell divisible by n, until on his last trip he had only to turn the key in the final cell.

What were the numbers of the cells whose doors were open at the end of this procedure and whose prisoners were set free?