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

\(\ds \)

\(=\)

\(\ds 6 \times 14\)

\(\ds \)

\(=\)

\(\ds 84\)

$\blacksquare$