Divisor Sum of Non-Square Semiprime/Examples/22/Proof 2
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Example of Divisor Sum of Non-Square Semiprime
- $\map {\sigma_1} {22} = 36$
Proof
We have that:
- $22 = 2 \times 11$
and so by definition is a semiprime whose prime factors are distinct.
Hence:
\(\ds \map {\sigma_1} {22}\) | \(=\) | \(\ds \paren {2 + 1} \paren {11 + 1}\) | Divisor Sum of Non-Square Semiprime | |||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times 12\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 3 \times \paren {2^2 \times 3}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^2 \times 3^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \paren {2 \times 3}^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 6^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 36\) |
$\blacksquare$