Divisor Sum of 459,818,240

Example of Divisor Sum of Integer

$\map {\sigma_1} {459 \, 818 \, 240} = 1 \, 379 \, 454 \, 720$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$459 \, 818 \, 240 = 2^8 \times 5 \times 7 \times 19 \times 37 \times 73$

Hence:

$\ds \map {\sigma_1} {459 \, 818 \, 240}$

$=$

$\ds \frac {2^9 - 1} {2 - 1} \times \paren {5 + 1} \times \paren {7 + 1} \times \paren {19 + 1} \times \paren {37 + 1} \times \paren {73 + 1}$

$\ds $

$=$

$\ds 511 \times 6 \times 8 \times 20 \times 38 \times 74$

$\ds $

$=$

$\ds \paren {7 \times 73} \times \paren {2 \times 3} \times 2^3 \times \paren {2^2 \times 5} \times \paren {2 \times 19} \times \paren {2 \times 37}$

$\ds $

$=$

$\ds 2^8 \times 3 \times 5 \times 7 \times 19 \times 37 \times 73$

$\ds $

$=$

$\ds 3 \times \paren {2^8 \times 5 \times 7 \times 19 \times 37 \times 73}$

$\ds $

$=$

$\ds 1 \, 379 \, 454 \, 720$

$\blacksquare$