Divisor Sum of 16,695

Example of Divisor Sum of Integer

$\map {\sigma_1} {16 \, 695} = 33 \, 696$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$16 \, 695 = 3^2 \times 5 \times 7 \times 53$

Hence:

$\ds \map {\sigma_1} {16 \, 695}$

$=$

$\ds \dfrac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {7 + 1} \times \paren {53 + 1}$

$\ds $

$=$

$\ds \dfrac {26} 2 \times 6 \times 8 \times 54$

$\ds $

$=$

$\ds 13 \times 6 \times 8 \times 54$

$\ds $

$=$

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

$\ds $

$=$

$\ds 2^5 \times 3^4 \times 13$

$\ds $

$=$

$\ds 33 \, 696$

$\blacksquare$