KöMaL 2019 K632

A father had a basket of plums. He gave the plums to his sons in the following way: the first son received 2 pieces plus one $n$th of the remaining plums, then the second son received 4 pieces plus one $n$th of the remaining plums, then the third one received 6 pieces plus one $n$th of the remaining plums, and so on. The rest of the plums the father kept for himself. At the end of this process, it turned out that everyone got the same number of plums. Given that the father had at least 2 sons, what may be the value of $n$?