Divisor Sum of 17,325

Example of Divisor Sum of Integer

$\map {\sigma_1} {17 \, 325} = 38 \, 688$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$17 \, 325 = 3^2 \times 5^2 \times 7 \times 11$

Hence:

$\ds \map {\sigma_1} {17 \, 325}$

$=$

$\ds \dfrac {3^3 - 1} {3 - 1} \times \dfrac {5^3 - 1} {5 - 1} \times \paren {7 + 1} \times \paren {11 + 1}$

$\ds $

$=$

$\ds \dfrac {26} 2 \times \dfrac {124} 4 \times 8 \times 12$

$\ds $

$=$

$\ds 13 \times 31 \times 8 \times 12$

$\ds $

$=$

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

$\ds $

$=$

$\ds 2^5 \times 3 \times 13 \times 31$

$\ds $

$=$

$\ds 38 \, 688$

$\blacksquare$