Divisor Sum of 17,716
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {17 \, 716} = 32 \, 032$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $17 \, 716 = 2^2 \times 43 \times 103$
Hence:
\(\ds \map {\sigma_1} {17 \, 716}\) | \(=\) | \(\ds \frac {2^3 - 1} {2 - 1} \times \paren {43 + 1} \times \paren {103 + 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds 7 \times 44 \times 104\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 7 \times \paren {2^2 \times 11} \times \paren {2^3 \times 13}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^5 \times 7 \times 11 \times 13\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 32 \, 032\) |
$\blacksquare$