Positive spoof Lehmer factorizations

TL;DR

This paper explores special factorizations related to Lehmer's totient conjecture, providing algorithms to find all such factorizations with a limited number of factors, advancing understanding of this number theory problem.

Contribution

It introduces an algorithm to compute all nontrivial spoof Lehmer factorizations with a fixed number of factors and enumerates those with up to six factors.

Findings

Algorithm for spoof Lehmer factorizations developed

Complete enumeration for up to six factors achieved

Contributes to understanding of Lehmer's totient conjecture

Abstract

We investigate the integer solutions of Diophantine equations related to Lehmer's totient conjecture. We give an algorithm that computes all nontrivial spoof Lehmer factorizations with a fixed number of factors, and enumerate all nontrivial spoof Lehmer factorizations with 6 or fewer factors.