Counterexamples to a Conjecture by Alaoglu and Erd\H{o}s

TL;DR

This paper employs computational techniques to disprove a longstanding conjecture by Alaoglu and Erdős concerning the properties of superabundant numbers, challenging previous assumptions in number theory.

Contribution

The paper introduces computational methods that provide counterexamples to the conjecture, offering new insights into the behavior of superabundant numbers.

Findings

Counterexamples disprove the conjecture

Computational approach effectively identified exceptions

Challenges previous beliefs about superabundant numbers

Abstract

In this paper we use computational methods to disprove a conjecture by Alaoglu and Erd\H{o}s regarding the superabundant numbers.