Divisor Sum of 267
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Example of Divisor Sum of Non-Square Semiprime
- $\map {\sigma_1} {267} = 360$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $267 = 3 \times 89$
and so by definition is a semiprime whose prime factors are distinct.
Hence:
\(\ds \map {\sigma_1} {267}\) | \(=\) | \(\ds \paren {3 + 1} \paren {89 + 1}\) | Divisor Sum of Non-Square Semiprime | |||||||||||
\(\ds \) | \(=\) | \(\ds 4 \times 90\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^2 \times \paren {2 \times 3^2 \times 5}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^3 \times 3^2 \times 5\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 360\) |
$\blacksquare$