Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Exactly $3$-Deficient-Perfect Numbers   Let $n$ and $k$ be positive integers and $\sigma(n)$ the sum of all positive
divisors of $n$. We call $n$ an exactly $k$-deficient-perfect number with
deficient divisors $d_1, d_2, \ldots, d_k$ if $d_1, d_2, \ldots, d_k$ are
distinct proper divisors of $n$ and $\sigma (n)=2n-(d_1+d_2+\ldots + d_k)$. In
this article, we show that the only odd exactly $3$-deficient-perfect number
with at most two distinct prime factors is $1521=3^2 \cdot 13^2$.

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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: eess