Divisor Sum of Non-Square Semiprime/Examples/14/Proof 2

Example of Divisor Sum of Non-Square Semiprime

$\map {\sigma_1} {14} = 24$

Proof

We have that:

$14 = 2 \times 7$

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

Hence:

\(\ds \map {\sigma_1} {14}\)

\(=\)

\(\ds \paren {2 + 1} \paren {7 + 1}\)

Divisor Sum of Non-Square Semiprime

\(\ds \)

\(=\)

\(\ds 3 \times 8\)

\(\ds \)

\(=\)

\(\ds 24\)

$\blacksquare$