Divisor Sum of 1,476,304,896

Example of Divisor Sum of Integer

$\map {\sigma_1} {1 \, 476 \, 304 \, 896} = 4 \, 428 \, 914 \, 688$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$1 \, 476 \, 304 \, 896 = 2^{13} \times 3 \times 11 \times 43 \times 127$

Hence:

$\ds \map {\sigma_1} {1 \, 476 \, 304 \, 896}$

$=$

$\ds \frac {2^{14} - 1} {2 - 1} \times \paren {3 + 1} \times \paren {11 + 1} \times \paren {43 + 1} \times \paren {127 + 1}$

$\ds $

$=$

$\ds 16 \, 383 \times 4 \times 12 \times 44 \times 128$

$\ds $

$=$

$\ds \paren {3 \times 43 \times 127} \times 2^2 \times \paren {2^2 \times 3} \times \paren {2^2 \times 11} \times 2^7$

$\ds $

$=$

$\ds 2^{13} \times 3^2 \times 11 \times 43 \times 127$

$\ds $

$=$

$\ds 3 \times \paren {2^{13} \times 3 \times 11 \times 43 \times 127}$

$\ds $

$=$

$\ds 4 \, 428 \, 914 \, 688$

$\blacksquare$