Define f(n) to be the smallest integer such that for every positive divisor d|n, either n|d^{d} or d^d|n^{f(n)}. How many positive integers b < 1000 which are not squarefree satisfy the equation f(2023) \cdot f(b) = f(2023b)?
Define f(n) to be the smallest integer such that for every positive divisor d|n, either n|d^{d} or d^d|n^{f(n)}. How many positive integers b < 1000 which are not squarefree satisfy the equation f(2023) \cdot f(b) = f(2023b)?