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On certain rational perfect numbers

Abstract: We study equations of type $\sigma(n) = \dfrac{k+1}{k} \cdot n+a,$ where $a\in \{0, 1, 2, 3\},$ where $k$ and $n$ are positive integers, while $\sigma(n)$ denotes the sum of divisors of $n.$
Keywords: sum / divisors / dfrac / cdot / integers / equations / rational perfect numbers

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