Divisor Sum of Non-Square Semiprime/Examples/15/Proof 2

Example of Divisor Sum of Non-Square Semiprime

$\map {\sigma_1} {15} = 24$

Proof

We have that:

$15 = 3 \times 5$

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

Hence:

\(\ds \map {\sigma_1} {15}\)

\(=\)

\(\ds \paren {3 + 1} \paren {5 + 1}\)

Divisor Sum of Non-Square Semiprime

\(\ds \)

\(=\)

\(\ds 4 \times 6\)

\(\ds \)

\(=\)

\(\ds 24\)

$\blacksquare$