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

Jump to navigation
Jump to search

## 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 | ||||||||||

\(\displaystyle \) | \(=\) | \(\displaystyle 6 \times 24\) | |||||||||||

\(\displaystyle \) | \(=\) | \(\displaystyle \left({2 \times 3}\right) \times \left({2^3 \times 3}\right)\) | |||||||||||

\(\displaystyle \) | \(=\) | \(\displaystyle 2^4 \times 3^2\) | |||||||||||

\(\displaystyle \) | \(=\) | \(\displaystyle \left({2^2 \times 3}\right)^2\) | |||||||||||

\(\displaystyle \) | \(=\) | \(\displaystyle 12^2\) | |||||||||||

\(\displaystyle \) | \(=\) | \(\displaystyle 144\) |

$\blacksquare$