Feasible Numbers

A natural number $n$ is called feasible if there exist non-negative integers $a_{1},a_{2},...,a_{n}$ such that

$\frac{1}{2^{a_{1}}}+\frac{1}{2^{a_{2}}}+...+\frac{1}{2^{a_{n}}}=\frac{1}{3^{a_{1}}}+\frac{2}{3^{a_{2}}}+...+\frac{n}{3^{a_{n}}}=1$

Find the number of feasible numbers $n≤997$