Divisor Sum of 83,328

Example of Divisor Sum of Integer

$\map {\sigma_1} {83 \, 328} = 261 \, 120$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$83 \, 328 = 2^7 \times 3 \times 7 \times 31$

Hence:

$\ds \map {\sigma_1} {83 \, 328}$

$=$

$\ds \frac {2^8 - 1} {2 - 1} \times \paren {3 + 1} \times \paren {7 + 1} \times \paren {31 + 1}$

$\ds $

$=$

$\ds 255 \times 4 \times 8 \times 32$

$\ds $

$=$

$\ds \paren {3 \times 5 \times 17} \times 2^2 \times 2^3 \times 2^5$

$\ds $

$=$

$\ds 2^{10} \times 3 \times 5 \times 17$

$\ds $

$=$

$\ds 261 \, 120$

$\blacksquare$