Divisor Sum of 1,571,328

Example of Divisor Sum of Integer

$\map {\sigma_1} {1 \, 571 \, 328} = 5 \, 106 \, 816$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$1 \, 571 \, 328 = 2^9 \times 3^2 \times 11 \times 31$

Hence:

$\ds \map {\sigma_1} {1 \, 571 \, 328}$

$=$

$\ds \frac {2^{10} - 1} {2 - 1} \times \frac {3^3 - 1} {3 - 1} \times \paren {11 + 1} \times \paren {31 + 1}$

$\ds $

$=$

$\ds 1023 \times 13 \times 12 \times 32$

$\ds $

$=$

$\ds \paren {3 \times 11 \times 31} \times 13 \times \paren {2^2 \times 3} \times 2^5$

$\ds $

$=$

$\ds 2^7 \times 3^2 \times 11 \times 13 \times 31$

$\ds $

$=$

$\ds 5 \, 106 \, 816$

$\blacksquare$