# On primitive weird numbers of the form $2^k p q$

- Authors
- Type
- Preprint
- Publication Date
- Apr 07, 2015
- Submission Date
- Apr 07, 2015
- Identifiers
- arXiv ID: 1504.02761
- Source
- arXiv
- License
- Yellow
- External links

## Abstract

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.