Divisor Sum of 30

Example of Divisor Sum of Square-Free Integer

$\map {\sigma_1} {30} = 72$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$30 = 2 \times 3 \times 5$

Hence:

\(\ds \map {\sigma_1} {30}\)

\(=\)

\(\ds \paren {2 + 1} \paren {3 + 1} \paren {5 + 1}\)

Divisor Sum of Square-Free Integer

\(\ds \)

\(=\)

\(\ds 3 \times 4 \times 6\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 72\)

$\blacksquare$