Divisor Sum of 90
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {90} = 234$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $90 = 2 \times 3^2 \times 5$
Hence:
\(\ds \map {\sigma_1} {90}\) | \(=\) | \(\ds \paren {2 + 1} \times \frac {3^3 - 1} {3 - 1} \times \paren {5 + 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times \frac {26} 2 \times 6\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times 13 \times \paren {2 \times 3}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2 \times 3^2 \times 13\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 234\) |
$\blacksquare$