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 \(n≤997\)

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