Divisor Sum of 720

Example of Divisor Sum of Integer

$\map {\sigma_1} {720} = 2418$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$720 = 2^4 \times 3^2 \times 5$

Hence:

$\ds \map {\sigma_1} {720}$

$=$

$\ds \frac {2^5 - 1} {2 - 1} \times \frac {3^3 - 1} {3 - 1} \times \paren {5 + 1}$

$\ds $

$=$

$\ds \frac {31} 1 \times \frac {26} 2 \times 6$

$\ds $

$=$

$\ds 31 \times 13 \times \paren {2 \times 3}$

$\ds $

$=$

$\ds 2 \times 3 \times 13 \times 31$

$\ds $

$=$

$\ds 2418$

$\blacksquare$