Sigma Function of 1,175,265

Example of Sigma Function of Integer

$\map \sigma {1 \, 175 \, 265} = 2 \, 614 \, 248$

where $\sigma$ denotes the $\sigma$ function.

Proof

We have that:

$1 \, 175 \, 265 = 3^2 \times 5 \times 7^2 \times 13 \times 41$

Hence from Sigma Function of Integer:

 $\ds \map \sigma {1 \, 175 \, 265}$ $=$ $\ds \frac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \frac {7^3 - 1} {7 - 1} \times \paren {13 + 1} \times \paren {41 + 1}$ $\ds$ $=$ $\ds \frac {26} 2 \times 6 \times \frac {342} 6 \times 14 \times 42$ $\ds$ $=$ $\ds 13 \times 6 \times 57 \times 14 \times 42$ $\ds$ $=$ $\ds 13 \times \paren {2 \times 3} \times \paren {3 \times 19} \times \paren {2 \times 7} \times \paren {2 \times 3 \times 7}$ $\ds$ $=$ $\ds 2^3 \times 3^3 \times 7^2 \times 13 \times 19$ $\ds$ $=$ $\ds 2 \, 614 \, 248$

$\blacksquare$