Divisor Sum of 8505

Example of Divisor Sum of Integer

$\map {\sigma_1} {8505} = 17 \, 472$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$8505 = 3^5 \times 5 \times 7$

Hence:

$\ds \map {\sigma_1} {8505}$

$=$

$\ds \dfrac {3^6 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {7 + 1}$

$\ds $

$=$

$\ds \dfrac {728} 2 \times 6 \times 8$

$\ds $

$=$

$\ds 364 \times 6 \times 8$

$\ds $

$=$

$\ds \paren {2^2 \times 7 \times 13} \times \paren {2 \times 3} \times 2^3$

$\ds $

$=$

$\ds 2^6 \times 3 \times 7 \times 13$

$\ds $

$=$

$\ds 17 \, 472$

$\blacksquare$