Divisor Sum of 8415

Example of Divisor Sum of Integer

$\map {\sigma_1} {8415} = 16 \, 848$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$8415 = 3^2 \times 5 \times 11 \times 17$

Hence:

$\ds \map {\sigma_1} {8415}$

$=$

$\ds \dfrac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {11 + 1} \times \paren {17 + 1}$

$\ds $

$=$

$\ds \dfrac {26} 2 \times 6 \times 12 \times 18$

$\ds $

$=$

$\ds 13 \times 6 \times 12 \times 18$

$\ds $

$=$

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

$\ds $

$=$

$\ds 2^4 \times 3^4 \times 13$

$\ds $

$=$

$\ds 16 \, 848$

$\blacksquare$