Divisor Sum of 32,665,894,275

Example of Divisor Sum of Integer

$\map {\sigma_1} {32 \, 665 \, 894 \, 275} = 64 \, 795 \, 852 \, 800$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$32 \, 665 \, 894 \, 275 = 3 \times 5^2 \times 7 \times 31 \times 59 \times 34 \, 019$

$\ds \map {\sigma_1} {32 \, 665 \, 894 \, 275}$

$=$

$\ds \paren {3 + 1} \times \frac {5^3 - 1} {5 - 1} \times \paren {7 + 1} \times \paren {31 + 1} \times \paren {59 + 1} \times \paren {34 \, 019 + 1}$

$\ds $

$=$

$\ds 4 \times \frac {124} 4 \times 8 \times 32 \times 60 \times 34 \, 020$

$\ds $

$=$

$\ds 4 \times 31 \times 8 \times 32 \times 60 \times 34 \, 020$

$\ds $

$=$

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

$\ds $

$=$

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

$\ds $

$=$

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

$\blacksquare$