Question 92
For any positive integer $n$, consider its binary representation. Denote by $f(n)$ the number we get after removing all the 0's in its binary representation, and $g(n)$ the number of 1's in the binary representation. For example, $f(19) = 7$ and $g(19) = 3$. Find all positive integers $n$ that satisfy $n = f(n)^{g(n)}$.