Divisor Sum of 33,075

Example of Divisor Sum of Integer

$\map {\sigma_1} {33 \, 075} = 70 \, 680$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$33 \, 075 = 3^3 \times 5^2 \times 7^2$

Hence:

$\ds \map {\sigma_1} {33 \, 075}$

$=$

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

$\ds $

$=$

$\ds \dfrac {80} 2 \times \dfrac {124} 4 \times \dfrac {342} 6$

$\ds $

$=$

$\ds 40 \times 31 \times 57$

$\ds $

$=$

$\ds \paren {2^3 \times 5} \times 31 \times \paren {3 \times 19}$

$\ds $

$=$

$\ds 2^3 \times 3 \times 5 \times 19 \times 31$

$\ds $

$=$

$\ds 70 \, 680$

$\blacksquare$