Divisor Sum of 34,883,817,075

Example of Divisor Sum of Integer

$\map {\sigma_1} {34 \, 883 \, 817 \, 075} = 64 \, 795 \, 852 \, 800$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$34 \, 883 \, 817 \, 075 = 3^3 \times 5^2 \times 127 \times 503 \times 809$

$\ds \map {\sigma_1} {34 \, 883 \, 817 \, 075}$

$=$

$\ds \frac {3^4 - 1} {3 - 1} \times \frac {5^3 - 1} {5 - 1} \times \paren {127 + 1} \times \paren {503 + 1} \times \paren {809 + 1}$

$\ds $

$=$

$\ds \frac {80} 2 \times \frac {124} 4 \times 128 \times 504 \times 810$

$\ds $

$=$

$\ds 40 \times 31 \times 128 \times 504 \times 810$

$\ds $

$=$

$\ds \paren {2^3 \times 5} \times 31 \times 2^7 \times \paren {2^3 \times 3^2 \times 7} \times \paren {2 \times 3^4 \times 5}$

$\ds $

$=$

$\ds 2^{14} \times 3^6 \times 5^2 \times 7 \times 31$

$\ds $

$=$

$\ds 64 \, 795 \, 852 \, 800$

$\blacksquare$