Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Abundancy Index and Feebly Amicable Numbers   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.

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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: astro-ph