Divisor Sum of 7425

Example of Divisor Sum of Integer

$\map {\sigma_1} {7425} = 14 \, 880$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$7425 = 3^3 \times 5^2 \times 11$

Hence:

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

$=$

$\ds \dfrac {3^4 - 1} {3 - 1} \times \dfrac {5^3 - 1} {5 - 1} \times \paren {11 + 1}$

$\ds $

$=$

$\ds \dfrac {80} 2 \times \dfrac {124} 4 \times 12$

$\ds $

$=$

$\ds 40 \times 31 \times 12$

$\ds $

$=$

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

$\ds $

$=$

$\ds 2^5 \times 3 \times 5 \times 31$

$\ds $

$=$

$\ds 14 \, 880$

$\blacksquare$