Divisor Sum of 60

Example of Divisor Sum of Integer

$\map {\sigma_1} {60} = 168$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$60 = 2^2 \times 3 \times 5$

Hence:

\(\ds \map {\sigma_1} {60}\)

\(=\)

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

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds \frac 7 1 \times 4 \times 6\)

\(\ds \)

\(=\)

\(\ds 2^3 \times 3 \times 7\)

\(\ds \)

\(=\)

\(\ds 168\)

$\blacksquare$