Divisor Sum of 31,704

Example of Divisor Sum of Integer

$\map {\sigma_1} {31 \, 704} = 79 \, 320$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$31 \, 704 = 2^3 \times 3 \times 1321$

Hence:

$\ds \map {\sigma_1} {31 \, 704}$

$=$

$\ds \frac {2^4 - 1} {2 - 1} \times \paren {3 + 1} \times \paren {1321 + 1}$

$\ds $

$=$

$\ds 15 \times 4 \times 1322$

$\ds $

$=$

$\ds \paren {3 \times 5} \times 2^2 \times \paren {2 \times 661}$

$\ds $

$=$

$\ds 2^3 \times 3 \times 5 \times 661$

$\ds $

$=$

$\ds 79 \, 320$

$\blacksquare$