Divisor Sum of 33,100,200,525

Example of Divisor Sum of Integer

$\map {\sigma_1} {33 \, 100 \, 200 \, 525} = 64 \, 795 \, 852 \, 800$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$33 \, 100 \, 200 \, 525 = 3 \times 5^2 \times 7 \times 29 \times 971 \times 2239$

$\ds \map {\sigma_1} {33 \, 100 \, 200 \, 525}$

$=$

$\ds \paren {3 + 1} \times \frac {5^3 - 1} {5 - 1} \times \paren {7 + 1} \times \paren {29 + 1} \times \paren {971 + 1} \times \paren {2239 + 1}$

$\ds $

$=$

$\ds 4 \times \frac {124} 4 \times 8 \times 30 \times 972 \times 2240$

$\ds $

$=$

$\ds 4 \times 31 \times 8 \times 30 \times 972 \times 2240$

$\ds $

$=$

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

$\ds $

$=$

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

$\ds $

$=$

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

$\blacksquare$