Consecutive Integers with Same Sigma/Examples

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Examples of Consecutive Integers with Same Sigma

Let $\sigma: \Z_{>0} \to \Z_{>0}$ denote the $\sigma$ function: the sum of all the positive integer divisors of $n$.

The following are solutions to the equation:

$\sigma \left({n}\right) = \sigma \left({n + 1}\right)$


$\sigma$ of $14$ equals $\sigma$ of $15$

$\map \sigma {14} = \map \sigma {15} = 24$


$\sigma$ of $206$ equals $\sigma$ of $207$

$\sigma \left({206}\right) = \sigma \left({207}\right) = 312$