Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Divisor sums representable as the sum of two squares   Let $s(n)$ denote the sum of the proper divisors of the natural number $n$.
We show that the number of $n \leq x$ such that $s(n)$ is a sum of two squares
has order of magnitude $x/\sqrt{\log x}$, which agrees with the count of $n
\leq x$ which are a sum of two squares. Our result confirms a special case of a
conjecture of Erd{\H o}s, Granville, Pomerance and Spiro, who in a 1990 paper
asserted that if $\mathcal{A} \subset \mathbb{N}$ has asymptotic density zero
(e.g. if $\mathcal{A}$ is the set of $n \leq x$ which are a sum of two
squares), then $s^{-1}(\mathcal{A})$ also has asymptotic density zero.

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The categories of this paper are: hep-ex
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
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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: hep-lat