Divisor Sum of 214

Example of Divisor Sum of Non-Square Semiprime

$\map {\sigma_1} {214} = 324$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$214 = 2 \times 107$

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

Hence:

\(\ds \map {\sigma_1} {214}\)

\(=\)

\(\ds \paren {2 + 1} \paren {107 + 1}\)

Divisor Sum of Non-Square Semiprime

\(\ds \)

\(=\)

\(\ds 3 \times 108\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 2^3 \times 3^4\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 18^2\)

\(\ds \)

\(=\)

\(\ds 324\)

$\blacksquare$