One-Step $G$-Unimprovable Numbers

Gennadiy Kalyabin

The infinitude is established of the set ${\mathbf{U}}_1$ of positive integers $N>5$ such that $G(N)\le \min (G(N/q),G(Np))$ where $q,p$ are primes, $q|N$ and $G(N):=\frac{σ(N)}{N\l…