Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Highest perfect power of a product of integers less than $x$   For $x\geq 3$, we define $w(x)$ as the highest integer $w$ for which there
exist integers $m, y\geq 1$ and $1\leq n_1<\dots<n_m\leq x$ such that
$n_1\cdots n_m=y^w$. We show that \[w(x)=x\exp\big(-(\sqrt{2}+o(1))\sqrt{\log
x\log\log x}\big).\]

15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio