Divisor Sum of 63

Example of Divisor Sum of Integer

$\map {\sigma_1} {63} = 104$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$63 = 3^2 \times 7$

Hence:

\(\ds \map {\sigma_1} {63}\)

\(=\)

\(\ds \frac {3^3 - 1} {3 - 1} \times \frac {7^2 - 1} {7 - 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds \frac {27 - 1} 2 \times \frac {49 - 1} 6\)

\(\ds \)

\(=\)

\(\ds 13 \times 8\)

\(\ds \)

\(=\)

\(\ds 104\)

$\blacksquare$