Divisor Sum of 17,955

Example of Divisor Sum of Integer

$\map {\sigma_1} {17 \, 955} = 38 \, 400$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$17 \, 955 = 3^3 \times 5 \times 7 \times 19$

Hence:

$\ds \map {\sigma_1} {17 \, 955}$

$=$

$\ds \dfrac {3^4 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {7 + 1} \times \paren {19 + 1}$

$\ds $

$=$

$\ds \dfrac {80} 2 \times 6 \times 8 \times 20$

$\ds $

$=$

$\ds 40 \times 6 \times 8 \times 20$

$\ds $

$=$

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

$\ds $

$=$

$\ds 2^9 \times 3 \times 5^2$

$\ds $

$=$

$\ds 38 \, 400$

$\blacksquare$