Let $α \geq 1$ . Is there a sequence of integers $n_{k}, m_{k}$ such that $n_{k} / m_{k} \to α$ and $σ (n_{k}) = σ (m_{k})$ for all $k \geq 1$ , where $σ$ is the sum of divisors function?

Worked, still open.

number theory · solved · 0 attempts

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