Some New Results On Even Almost Perfect Numbers Which Are Not Powers Of Two

TL;DR

This paper investigates even almost perfect numbers that are not powers of two, providing new inequalities and properties that advance understanding of their structure and constraints.

Contribution

It introduces new bounds and properties for even almost perfect numbers not of the form 2^k, expanding theoretical knowledge in number theory.

Findings

Proves that 2^{r+1} < b for certain almost perfect numbers

Establishes inequalities relating powers of two and other factors in these numbers

Contributes to the classification and understanding of even almost perfect numbers

Abstract

In this note, we present some new results on even almost perfect numbers which are not powers of two. In particular, we show that $2^{r+1} < b$, if ${2^r}{b^2}$ is an even almost perfect number.