Some results concerning odd numbers of the form 6k-1 and Fermat numbers

In this work, one presents some results concerning odd numbers of the form 6k-1 and Fermat numbers using a new approach. Using this novel approach, one proves also that all odd numbers of the form 6k-1 and Fermat numbers are never perfect. In addition, one proves for the first time that all odd numbers of the form 6k-1 and Fermat numbers are never superperfect nor Descartes number, not quasiperfect and nor almost perfect. The case of near-perfect number is also considered in this study, where it is proved that all odd numbers of the form 6k-1 and Fermat numbers are never near-perfect.