# Analysis of the Ratio $D(n)/n$

## TL;DR

This paper explores the properties of the deficiency index, defined as the ratio D(n)/n, and discusses related concepts using the deficiency index framework, drawing parallels with the abundancy index.

## Contribution

It introduces the deficiency index as a new perspective and recasts existing concepts in this framework, providing fresh insights into number theoretic ratios.

## Key findings

- Properties of the deficiency index are analyzed.
- Connections between deficiency index and abundancy index are established.
- New conceptual recast of number theoretic ratios is proposed.

## Abstract

In this note, we investigate properties of the ratio $D(n)/n$, which we will call the deficiency index. We will discuss some concepts recast in the language of the deficiency index, based on similar considerations in terms of the abundancy index.