Divisor Sum of 26,775

Example of Divisor Sum of Integer

$\map {\sigma_1} {26 \, 775} = 58 \, 032$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$26 \, 775 = 3^2 \times 5^2 \times 7 \times 17$

Hence:

$\ds \map {\sigma_1} {26 \, 775}$

$=$

$\ds \dfrac {3^3 - 1} {3 - 1} \times \dfrac {5^3 - 1} {5 - 1} \times \paren {7 + 1} \times \paren {17 + 1}$

$\ds $

$=$

$\ds \dfrac {26} 2 \times \dfrac {124} 4 \times 8 \times 18$

$\ds $

$=$

$\ds 13 \times 31 \times 8 \times 18$

$\ds $

$=$

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

$\ds $

$=$

$\ds 2^4 \times 3^2 \times 13 \times 31$

$\ds $

$=$

$\ds 58 \, 032$

$\blacksquare$