Overpowered Divisors

The [Fundamental Theorem of Arithmetic](https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic) states that every number can be represented uniquely by its prime factorization, which is the decomposition of the number into the product of its prime powers. Formally, the prime factorization of a number $N = p_1^{q_1} \times p_2^{q_2} \times p_3^{q_3} \dots \times p_m^{q_m}$, where $p_1, p_