Divisor Sum of 1,175,265

Example of Divisor Sum of Integer

$\map {\sigma_1} {1 \, 175 \, 265} = 2 \, 614 \, 248$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$1 \, 175 \, 265 = 3^2 \times 5 \times 7^2 \times 13 \times 41$

$\ds \map {\sigma_1} {1 \, 175 \, 265}$

$=$

$\ds \frac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \frac {7^3 - 1} {7 - 1} \times \paren {13 + 1} \times \paren {41 + 1}$

$\ds $

$=$

$\ds \frac {26} 2 \times 6 \times \frac {342} 6 \times 14 \times 42$

$\ds $

$=$

$\ds 13 \times 6 \times 57 \times 14 \times 42$

$\ds $

$=$

$\ds 13 \times \paren {2 \times 3} \times \paren {3 \times 19} \times \paren {2 \times 7} \times \paren {2 \times 3 \times 7}$

$\ds $

$=$

$\ds 2^3 \times 3^3 \times 7^2 \times 13 \times 19$

$\ds $

$=$

$\ds 2 \, 614 \, 248$

$\blacksquare$