Divisor Sum of 836

Example of Divisor Sum of Integer

$\map {\sigma_1} {836} = 1680$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$836 = 2^2 \times 11 \times 19$

Hence:

$\ds \map {\sigma_1} {836}$

$=$

$\ds \frac {2^3 - 1} {2 - 1} \times \paren {11 + 1} \times \paren {19 + 1}$

$\ds $

$=$

$\ds \frac 7 1 \times 12 \times 20$

$\ds $

$=$

$\ds 7 \times \paren {2^2 \times 3} \times \paren {2^2 \times 5}$

$\ds $

$=$

$\ds 2^4 \times 3 \times 5 \times 7$

$\ds $

$=$

$\ds 1680$

$\blacksquare$