Divisor Sum of 120

Example of Divisor Sum of Integer

$\map {\sigma_1} {120} = 360$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$120 = 2^3 \times 3 \times 5$

Hence:

\(\ds \map {\sigma_1} {120}\)

\(=\)

\(\ds \frac {2^4 - 1} {2 - 1} \times \paren {3 + 1} \times \paren {5 + 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds \frac {15} 1 \times 4 \times 6\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 360\)

$\blacksquare$