Divisor Sum of 4725

Example of Divisor Sum of Integer

$\map {\sigma_1} {4725} = 9920$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$4725 = 3^3 \times 5^2 \times 7$

Hence:

$\ds \map {\sigma_1} {4725}$

$=$

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

$\ds $

$=$

$\ds \dfrac {80} 2 \times \dfrac {124} 4 \times 8$

$\ds $

$=$

$\ds 40 \times 31 \times 8$

$\ds $

$=$

$\ds \paren {2^3 \times 5} \times 31 \times 2^3$

$\ds $

$=$

$\ds 2^6 \times 5 \times 31$

$\ds $

$=$

$\ds 9920$

$\blacksquare$