Divisor Sum of 323

Example of Divisor Sum of Non-Square Semiprime

$\map {\sigma_1} {323} = 360$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$323 = 17 \times 19$

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

Hence:

\(\ds \map {\sigma_1} {323}\)

\(=\)

\(\ds \paren {17 + 1} \paren {19 + 1}\)

Divisor Sum of Non-Square Semiprime

\(\ds \)

\(=\)

\(\ds 18 \times 20\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 360\)

$\blacksquare$