Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Diophantine equation
  $\sigma_{2}(\overline{X}_{n})=\sigma_{n}(\overline{X}_{n})$   In this note we investigate the set $S(n)$ of positive integer solutions of
the title Diophantine equation. In particular, for a given $n$ we prove
boundedness of the number of solutions, give precise upper bound on the common
value of $\sigma_{2}(\overline{X}_{n})$ and $\sigma_{n}(\overline{X}_{n})$
together with the biggest value of the variable $x_{n}$ appearing in the
solution. Moreover, we enumerate all solutions for $n\leq 16$ and discuss the
set of values of $x_{n}/x_{n-1}$ over elements of $S(n)$.

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The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an