Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arithmetic properties of the sum of divisors   The divisor function $\sigma(n)$ denotes the sum of the divisors of the
positive integer $n$. For a prime $p$ and $m \in \mathbb{N}$, the $p$-adic
valuation of $m$ is the highest power of $p$ which divides $m$. Formulas for
$\nu_{p}(\sigma(n))$ are established. For $p=2$, these involve only the odd
primes dividing $n$. These expressions are used to establish the bound
$\nu_{2}(\sigma(n)) \leq \lceil\log_{2}(n) \rceil$, with equality if and only
if $n$ is the product of distinct Mersenne primes, and for an odd prime $p$,
the bound is $\nu_{p}(\sigma(n)) \leq \lceil \log_{p}(n) \rceil$, with equality
related to solutions of the Ljunggren-Nagell diophantine equation.

1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas