Divisor Sum of 56
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {56} = 120$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $56 = 2^3 \times 7$
Hence:
\(\ds \map {\sigma_1} {56}\) | \(=\) | \(\ds \frac {2^4 - 1} {2 - 1} \times \frac {7^2 - 1} {7 - 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac {16 - 1} 1 \times \frac {49 - 1} 6\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 15 \times 8\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {3 \times 5} \times 2^3\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 120\) |
$\blacksquare$