Sigma Function of 2556

From ProofWiki
(Redirected from Sigma of 2556)
Jump to navigation Jump to search

Example of Sigma Function of Integer

$\sigma \left({2556}\right) = 6552$

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


Proof

We have that:

$2556 = 2^2 \times 3^2 \times 71$

Hence:

\(\displaystyle \sigma \left({2556}\right)\) \(=\) \(\displaystyle \frac {2^3 - 1} {2 - 1} \times \frac {3^3 - 1} {3 - 1} \times \left({71 + 1}\right)\) Sigma Function of Integer
\(\displaystyle \) \(=\) \(\displaystyle \frac 7 1 \times \frac {26} 2 \times 72\)
\(\displaystyle \) \(=\) \(\displaystyle 7 \times 13 \times \left({2^3 \times 3^2}\right)\)
\(\displaystyle \) \(=\) \(\displaystyle 2^3 \times 3^2 \times 7 \times 13\)
\(\displaystyle \) \(=\) \(\displaystyle 6552\)

$\blacksquare$