Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On exponentially coprime integers   The integers $n=\prod_{i=1}^r p_i^{a_i}$ and $m=\prod_{i=1}^r p_i^{b_i}$
having the same prime factors are called exponentially coprime if $(a_i,b_i)=1$
for every $1\le i\le r$. We estimate the number of pairs of exponentially
coprime integers $n,m\le x$ having the prime factors $p_1,...,p_r$ and show
that the asymptotic density of pairs of exponentially coprime integers having
$r$ fixed prime divisors is $(\zeta(2))^{-r}$.

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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: physics