On Anti-Sociable Numbers of Special Form
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A positive integer $n$ is called an anti-sociable number if there is no positive integer $m$ such that $\sigma(n) = \sigma(m) = n + m$. By applying an elementary approach, we show that any number of the form $p^k$ is an anti-sociable number, where $p$ is a prime and $k \leq 32$ is a positive integer.
