Divisor Sum of 87

Example of Divisor Sum of Non-Square Semiprime

$\map {\sigma_1} {87} = 120$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$87 = 3 \times 29$

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

Hence:

\(\ds \map {\sigma_1} {115}\)

\(=\)

\(\ds \paren {3 + 1} \paren {29 + 1}\)

Divisor Sum of Non-Square Semiprime

\(\ds \)

\(=\)

\(\ds 4 \times 30\)

\(\ds \)

\(=\)

\(\ds 2^2 \times \paren {2 \times 3 \times 5}\)

\(\ds \)

\(=\)

\(\ds 2^3 \times 3 \times 5\)

\(\ds \)

\(=\)

\(\ds 120\)

$\blacksquare$