Question 14
Find all natural numbers $n$ for which there are nonnegative integers $a_1,\ldots,a_n$ such that
$$\frac1{2a_1}+\frac1{2a_2}+\cdots+\frac1{2a_n}=\frac1{3a_1}+\frac1{3a_2}+\cdots+\frac n{3a_n}=1.$$
$$\frac1{2a_1}+\frac1{2a_2}+\cdots+\frac1{2a_n}=\frac1{3a_1}+\frac1{3a_2}+\cdots+\frac n{3a_n}=1.$$