Divisor Sum of 382

Example of Divisor Sum of Non-Square Semiprime

$\map {\sigma_1} {382} = 576$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$382 = 2 \times 191$

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

Hence:

\(\ds \map {\sigma_1} {382}\)

\(=\)

\(\ds \paren {2 + 1} \paren {191 + 1}\)

Divisor Sum of Non-Square Semiprime

\(\ds \)

\(=\)

\(\ds 3 \times 192\)

\(\ds \)

\(=\)

\(\ds 3 \times \paren {2^6 \times 3}\)

\(\ds \)

\(=\)

\(\ds 2^6 \times 3^2\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 24^2\)

\(\ds \)

\(=\)

\(\ds 576\)

$\blacksquare$