Disproofs of two conjectures concerning nondeficient numbers
Number Theory
2026-07-13 v1
Abstract
A positive integer is said to be nondeficient if . Letting the positive divisors of a positive integer be written as , and letting denote a set of integers, if there exist values such that , then is said to be an -perfect number. Ross, in 2024, introduced the study of -perfect numbers, and concluded with two conjectures that each concern both -perfect numbers and nondeficient numbers. We disprove both of these conjectures.
Cite
@article{arxiv.2607.11043,
title = {Disproofs of two conjectures concerning nondeficient numbers},
author = {John M. Campbell},
journal= {arXiv preprint arXiv:2607.11043},
year = {2026}
}
Comments
Submitted for publication