Sigma Function of 672

From ProofWiki
Jump to navigation Jump to search

Example of Sigma Function of Integer

$\map \sigma {672} = 2016$

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


Proof

We have that:

$672 = 2^5 \times 3 \times 7$


Hence:

\(\displaystyle \map \sigma {672}\) \(=\) \(\displaystyle \frac {2^6 - 1} {2 - 1} \times \paren {3 + 1} \times \paren {7 + 1}\) Sigma Function of Integer
\(\displaystyle \) \(=\) \(\displaystyle \frac {63} 1 \times 4 \times 8\)
\(\displaystyle \) \(=\) \(\displaystyle \paren {3^2 \times 7} \times 2^2 \times 2^3\)
\(\displaystyle \) \(=\) \(\displaystyle 2^5 \times 3^2 \times 7\)
\(\displaystyle \) \(=\) \(\displaystyle 2016\)

$\blacksquare$