Divisor Sum of 24,255

Example of Divisor Sum of Integer

$\map {\sigma_1} {24 \, 255} = 53 \, 352$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$24 \, 255 = 3^2 \times 5 \times 7^2 \times 11$

Hence:

$\ds \map {\sigma_1} {24 \, 255}$

$=$

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

$\ds $

$=$

$\ds \dfrac {26} 2 \times 6 \times \dfrac {342} 6 \times 12$

$\ds $

$=$

$\ds 13 \times 6 \times 57 \times 12$

$\ds $

$=$

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

$\ds $

$=$

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

$\ds $

$=$

$\ds 53 \, 352$

$\blacksquare$