Divisor Sum of 295,488

Example of Divisor Sum of Integer

$\map {\sigma_1} {295 \, 488} = 924 \, 560$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$295 \, 488 = 2^6 \times 3^5 \times 19$

Hence:

$\ds \map {\sigma_1} {295 \, 488}$

$=$

$\ds \frac {2^7 - 1} {2 - 1} \times \frac {3^6 - 1} {3 - 1} \times \paren {19 + 1}$

$\ds $

$=$

$\ds \frac {127} 1 \times \frac {728} 2 \times 20$

$\ds $

$=$

$\ds 127 \times 364 \times 20$

$\ds $

$=$

$\ds 127 \times \paren {2^2 \times 7 \times 13} \paren {2^2 \times 5}$

$\ds $

$=$

$\ds 2^4 \times 5 \times 7 \times 13 \times 127$

$\ds $

$=$

$\ds 924 \, 560$

$\blacksquare$