Divisor Sum of 265
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Example of Divisor Sum of Non-Square Semiprime
- $\map {\sigma_1} {265} = 324$
where $\sigma_1$ denotes the divisor sum function.
Proof
We have that:
- $265 = 5 \times 53$
Hence:
| \(\ds \map {\sigma_1} {265}\) | \(=\) | \(\ds \paren {5 + 1} \paren {53 + 1}\) | Divisor Sum of Non-Square Semiprime | |||||||||||
| \(\ds \) | \(=\) | \(\ds 6 \times 54\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {2 \times 3} \times \paren {2 \times 3^3}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 2^2 \times 3^4\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {2 \times 3^2}^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 18^2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 324\) |
$\blacksquare$