12 times Sigma of 12 equals 14 times Sigma of 14

Theorem

$x = 12$ and $y = 14$ are solutions to the indeterminate equation:

$x \ \sigma \left({x}\right) = y \ \sigma \left({y}\right)$

where $\sigma$ denotes the $\sigma$ function.

$\ds 12 \ \sigma \left({12}\right)$

$=$

$\ds 12 \times 28$

$\ds $

$=$

$\ds 12 \times 2 \times 14$

$\ds $

$=$

$\ds 14 \times 24$

$\ds $

$=$

$\ds 14 \ \sigma \left({14}\right)$

$\blacksquare$