Analysis of the ratio $D(n)/n$ (Reference request)

Question

In his undergraduate honors thesis at Penn State University, Kurt Ludwick analyzed the ratio $\sigma(n)/n$, where $\sigma = \sigma_{1}$ is the classical sum-of-divisors function. (His thesis was titled Analysis of the ratio $\sigma(n)/n$. I would have included a hyperlink if an online copy of the same was available. I did find the following hyperlink, but it appears to be broken: <https://www.math.temple.edu/~ludwick/thesis/thesisinfo.html>)

Here is my question:

Have similar theses/researches/studies been done on analyzing/investigating the nature of the ratio $D(n)/n$, where $D(n)=2n-\sigma(n)$ is the deficiency of $n \in \mathbb{N}$?

Notice that $$\dfrac{D(n)}{n}=\dfrac{2n-\sigma(n)}{n}=2-\dfrac{\sigma(n)}{n}.$$

Answer 1

From the abstract of the arXiv preprint titled Analysis of the Ratio $D(n)/n$:

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.