Divisor Sum of 360

Example of Divisor Sum of Integer

$\map {\sigma_1} {360} = 1170$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$360 = 2^3 \times 3^2 \times 5$

Hence:

\(\ds \map {\sigma_1} {360}\)

\(=\)

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

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds \frac {15} 1 \times \frac {26} 2 \times 6\)

\(\ds \)

\(=\)

\(\ds \paren {3 \times 5} \times 13 \times \paren {2 \times 3}\)

\(\ds \)

\(=\)

\(\ds 2 \times 3^2 \times 5 \times 13\)

\(\ds \)

\(=\)

\(\ds 1170\)

$\blacksquare$