Divisor Sum of 11,025

Example of Divisor Sum of Integer

$\map {\sigma_1} {11 \, 025} = 22 \, 971$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$11 \, 025 = 3^2 \times 5^2 \times 7^2$

Hence:

$\ds \map {\sigma_1} {11 \, 025}$

$=$

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

$\ds $

$=$

$\ds \dfrac {26} 2 \times \dfrac {124} 4 \times \dfrac {342} 6$

$\ds $

$=$

$\ds 13 \times 31 \times 57$

$\ds $

$=$

$\ds 13 \times 31 \times \paren {3 \times 19}$

$\ds $

$=$

$\ds 22 \, 971$

$\blacksquare$