Divisor Sum of 65

Example of Divisor Sum of Non-Square Semiprime

$\map {\sigma_1} {65} = 84$

where $\sigma_1$ denotes the divisor sum function.


Proof

We have that:

$65 = 5 \times 13$

and so by definition is a semiprime whose prime factors are distinct.


Hence:

\(\ds \map {\sigma_1} {65}\) \(=\) \(\ds \paren {5 + 1} \paren {13 + 1}\) Divisor Sum of Non-Square Semiprime
\(\ds \) \(=\) \(\ds 6 \times 14\)
\(\ds \) \(=\) \(\ds 84\)

$\blacksquare$

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