# Sigma Function of Non-Square Semiprime/Examples/115/Proof 2

## Example of Sigma Function of Non-Square Semiprime

$\sigma \left({115}\right) = 144$

## Proof

We have that:

$115 = 5 \times 23$

and so by definition is a semiprime whose prime factors are distinct.

Hence:

 $\displaystyle \sigma \left({115}\right)$ $=$ $\displaystyle \left({5 + 1}\right) \left({23 + 1}\right)$ Sigma Function of Non-Square Semiprime $\displaystyle$ $=$ $\displaystyle 6 \times 24$ $\displaystyle$ $=$ $\displaystyle \left({2 \times 3}\right) \times \left({2^3 \times 3}\right)$ $\displaystyle$ $=$ $\displaystyle 2^4 \times 3^2$ $\displaystyle$ $=$ $\displaystyle \left({2^2 \times 3}\right)^2$ $\displaystyle$ $=$ $\displaystyle 12^2$ $\displaystyle$ $=$ $\displaystyle 144$

$\blacksquare$