Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On primitive weird numbers of the form $2^k p q$   We say a natural number~$n$ is abundant if $\sigma(n)>2n$, where $\sigma(n)$
denotes the sum of the divisors of~$n$. The aliquot parts of~$n$ are those
divisors less than~$n$, and we say that an abundant number~$n$ is pseudoperfect
if there is some subset of the aliquot parts of~$n$ which sum to~$n$. We
say~$n$ is weird if~$n$ is abundant but not pseudoperfect. We call a weird
number~$n$ primitive if none of its aliquot parts are weird. We find all
primitive weird numbers of the form $2^kpq$ ($p<q$ being odd primes) for $1\le
k\le14$. We also find primitive weird numbers of the same form, larger than any
previously published.

11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom