Divisor Sum of 304

Example of Divisor Sum of Integer

$\map {\sigma_1}{304} = 620$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$304 = 2^4 \times 19$

Hence:

\(\ds \map {\sigma_1} {304}\)

\(=\)

\(\ds \frac {2^5 - 1} {2 - 1} \times \frac {19^2 - 1} {19 - 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds \frac {31 - 1} 1 \times \frac {361 - 1} {18}\)

\(\ds \)

\(=\)

\(\ds 31 \times 20\)

\(\ds \)

\(=\)

\(\ds \paren {2^2 \times 5} \times 31\)

\(\ds \)

\(=\)

\(\ds 620\)

$\blacksquare$