Divisor Sum of 1638

Example of Divisor Sum of Integer

$\map {\sigma_1} {1638} = 4368$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$1638 = 2 \times 3^2 \times 7 \times 13$

Hence:

$\ds \map {\sigma_1} {1638}$

$=$

$\ds \paren {2 + 1} \frac {3^3 - 1} {3 - 1} \times \paren {7 + 1} \times \paren {13 + 1}$

$\ds $

$=$

$\ds 3 \times \frac {26} 2 \times 8 \times 14$

$\ds $

$=$

$\ds 3 \times 13 \times 2^3 \times \paren {2 \times 7}$

$\ds $

$=$

$\ds 2^4 \times 3 \times 7 \times 13$

$\ds $

$=$

$\ds 4368$

$\blacksquare$