Determining all biunitary triperfect numbers of a certain form

TL;DR

This paper proves that 2160 is the only biunitary triperfect number divisible by 27, providing a complete characterization of such numbers within this form.

Contribution

It establishes the uniqueness of 2160 as the only biunitary triperfect number divisible by 27, advancing understanding of triperfect numbers with biunitary divisibility.

Findings

2160 is the only biunitary triperfect number divisible by 27

The paper confirms the uniqueness of this number within the specified form

Provides a complete classification for this subset of triperfect numbers

Abstract

We shall show that $2160$ is the only biunitary triperfect number divisible by $27=3^3$.