Divisor Sum of 51,001,180,160

Example of Divisor Sum of Integer

$\map {\sigma_1} {51 \, 001 \, 180 \, 160} = 153 \, 003 \, 540 \, 480$

where $\sigma_1$ denotes the divisor sum function.

We have that:

$51 \, 001 \, 180 \, 160 = 2^{14} \times 5 \times 7 \times 19 \times 31 \times 151$

Hence:

$\ds \map {\sigma_1} {51 \, 001 \, 180 \, 160}$

$=$

$\ds \frac {2^{15} - 1} {2 - 1} \times \paren {5 + 1} \times \paren {7 + 1} \times \paren {19 + 1} \times \paren {31 + 1} \times \paren {151 + 1}$

$\ds $

$=$

$\ds 32 \, 767 \times 6 \times 8 \times 20 \times 32 \times 152$

$\ds $

$=$

$\ds \paren {7 \times 31 \times 151} \times \paren {2 \times 3} \times 2^3 \times \paren {2^2 \times 5} \times 2^5 \times \paren {2^3 \times 19}$

$\ds $

$=$

$\ds 2^{14} \times 3 \times 5 \times 7 \times 19 \times 31 \times 151$

$\ds $

$=$

$\ds 3 \times \paren {2^{14} \times 5 \times 7 \times 19 \times 31 \times 151}$

$\ds $

$=$

$\ds 153 \, 003 \, 540 \, 480$

$\blacksquare$