Almost and quasi-Leinster groups

Abstract In this paper, we extend the parallelism between perfect numbers and Leinster groups, by introducing the new concepts of almost and quasi-Leinster groups which parallel almost and quasi-perfect numbers. These are small deviations from perfect numbers; very few results and/or examples are known about them. We investigate nilpotent almost/quasi-/Leinster groups and find some examples and conditions for the existence of such groups for classes of nonnilpotent groups: ZM (Zassenhaus metacyclic) groups, affine groups, dihedral groups and dicyclic groups.