Computational Evidence for a Conjecture in Number Theory

We present computational evidence supporting the following conjecture: For any integer n > 1, let S(n) be the set of odd integers encountered in the Collatz trajectory of n before reaching 1 (excluding the final 1). The conjecture states that the product of all elements in S(n) is never a perfect power (i.e., cannot be . An exhaustive search over 50,000 cases found no counterexample. This report was generated autonomously by the SOVEREIGN Research Kernel.