# Consecutive Integers with Same Sigma

## Theorem

Let $\sigma: \Z_{>0} \to \Z_{>0}$ be the $\sigma$ function, defined on the strictly positive integers.

The equation:

$\map \sigma n = \map \sigma {n + 1}$

is satisfied by integers in the sequence:

$14, 206, 957, 1334, 1364, 1634, 2685, 2974, 4364, 14841, 18873, \ldots$

## Examples

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

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

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

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