Divisor Sum of 1980
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Example of Divisor Sum of Integer
- $\map {\sigma_1} {1980} = 6552$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $1980 = 2^2 \times 3^2 \times 5 \times 11$
Hence:
\(\ds \map {\sigma_1} {1980}\) | \(=\) | \(\ds \frac {2^3 - 1} {2 - 1} \times \frac {3^3 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {11 + 1}\) | Divisor Sum of Integer | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac 7 1 \times \frac {26} 2 \times 6 \times 12\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 7 \times 13 \times \paren {2 \times 3} \times \paren {2^2 \times 3}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^3 \times 3^2 \times 7 \times 13\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 6552\) |
$\blacksquare$