Erdős conjectured that every odd number greater than one can be expressed as the sum of a squarefree number and a power of two. Subsequently, Odlyzko and McCranie provided numerical verification of this conjecture up to 10⁷ and 1.4 · 10⁹. In this paper, we extend the verification to all odd integers up to 2⁵⁰, thereby improving the previous bound by a factor of more than 8 · 10⁵. Our approach employs a highly parallelized algorithm implemented on a GPU, which significantly accelerates the process. We provide details of the algorithm and present novel heuristic computations and numerical findings, including the smallest odd numbers < 2⁵⁰ that require a higher power of two than all smaller ones in their representation.