Divisor Sum of 2205

Example of Divisor Sum of Integer

$\map {\sigma_1} {2205} = 4446$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$2205 = 3^2 \times 5 \times 7^2$

Hence:

$\ds \map {\sigma_1} {2205}$

$=$

$\ds \dfrac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \dfrac {7^3 - 1} {7 - 1}$

$\ds $

$=$

$\ds \dfrac {26} 2 \times 6 \times \dfrac {342} 6$

$\ds $

$=$

$\ds 13 \times 6 \times 57$

$\ds $

$=$

$\ds 13 \times \paren {2 \times 3} \times \paren {3 \times 19}$

$\ds $

$=$

$\ds 2 \times 3^2 \times 13 \times 19$

$\ds $

$=$

$\ds 4446$

$\blacksquare$