Divisor Sum of 20,475

Example of Divisor Sum of Integer

$\map {\sigma_1} {20 \, 475} = 45 \, 136$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$20 \, 475 = 3^2 \times 5^2 \times 7 \times 13$

Hence:

$\ds \map {\sigma_1} {20 \, 475}$

$=$

$\ds \dfrac {3^3 - 1} {3 - 1} \times \dfrac {5^3 - 1} {5 - 1} \times \paren {7 + 1} \times \paren {13 + 1}$

$\ds $

$=$

$\ds \dfrac {26} 2 \times \dfrac {124} 4 \times 8 \times 14$

$\ds $

$=$

$\ds 13 \times 31 \times 8 \times 14$

$\ds $

$=$

$\ds 13 \times 31 \times 2^3 \times \paren {2 \times 7}$

$\ds $

$=$

$\ds 2^4 \times 7 \times 13 \times 31$

$\ds $

$=$

$\ds 45 \, 136$

$\blacksquare$