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

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Preprint
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Submission Date
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arXiv ID: 1504.02761
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arXiv
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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.

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