Divisor Sum of 56

Example of Divisor Sum of Integer

$\map {\sigma_1} {56} = 120$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$56 = 2^3 \times 7$

Hence:

\(\ds \map {\sigma_1} {56}\)

\(=\)

\(\ds \frac {2^4 - 1} {2 - 1} \times \frac {7^2 - 1} {7 - 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds \frac {16 - 1} 1 \times \frac {49 - 1} 6\)

\(\ds \)

\(=\)

\(\ds 15 \times 8\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 120\)

$\blacksquare$