Divisor Sum of 1257
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Example of Divisor Sum of Non-Square Semiprime
- $\map {\sigma_1} {1257} = 1680$
Proof
We have that:
- $1257 = 3 \times 419$
and so by definition is a semiprime whose prime factors are distinct.
Hence:
\(\ds \map {\sigma_1} {1257}\) | \(=\) | \(\ds \paren {3 + 1} \paren {419 + 1}\) | Divisor Sum of Non-Square Semiprime | |||||||||||
\(\ds \) | \(=\) | \(\ds 4 \times 420\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^2 \times \paren {2^2 \times 3 \times 5 \times 7}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 1680\) |
$\blacksquare$