Divisor Sum of 36

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Example of Divisor Sum of Integer

$\map {\sigma_1} {36} = 91$

where $\sigma_1$ denotes the divisor sum function.


Proof

We have that:

$36 = 2^2 \times 3^2$

Hence:

\(\ds \map {\sigma_1} {36}\) \(=\) \(\ds \frac {2^3 - 1} {2 - 1} \times \frac {3^3 - 1} {3 - 1}\) Divisor Sum of Integer
\(\ds \) \(=\) \(\ds \frac {8 - 1} 1 \times \frac {27 - 1} 2\)
\(\ds \) \(=\) \(\ds 7 \times 13\)
\(\ds \) \(=\) \(\ds 91\)

$\blacksquare$