Divisor Sum of 7875

Example of Divisor Sum of Integer

$\map {\sigma_1} {7875} = 16 \, 224$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$7875 = 3^2 \times 5^3 \times 7$

Hence:

$\ds \map {\sigma_1} {7875}$

$=$

$\ds \dfrac {3^3 - 1} {3 - 1} \times \dfrac {5^4 - 1} {5 - 1} \times \paren {7 + 1}$

$\ds $

$=$

$\ds \dfrac {26} 2 \times \dfrac {624} 4 \times 8$

$\ds $

$=$

$\ds 13 \times 156 \times 8$

$\ds $

$=$

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

$\ds $

$=$

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

$\ds $

$=$

$\ds 16 \, 224$

$\blacksquare$