  This research explores the sum of divisors - $\sigma(n)$ - and the abundancy
index given by the function $\frac{\sigma(n)}{n}$. We give a generalization of
amicable pairs - feebly amicable pairs (also known as harmonious pairs), that
is $m,n$ such that $\frac{n}{\sigma(n)}+ \frac{m}{\sigma(m)}=1$. We first give
some groundwork in introductory number theory, then the goal of the paper is to
determine if all numbers are feebly amicable with at least one other number by
using known results about the abundancy index. We establish that not all
numbers are feebly amicable with at least one other number. We generate data
using the R programming language and give some questions and conjectures.
