Divisor Sum of 42

Example of Divisor Sum of Square-Free Integer

$\map {\sigma_1} {42} = 96$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$42 = 2 \times 3 \times 7$

Hence:

\(\ds \map {\sigma_1} {42}\)

\(=\)

\(\ds \paren {2 + 1} \paren {3 + 1} \paren {7 + 1}\)

Divisor Sum of Square-Free Integer

\(\ds \)

\(=\)

\(\ds 3 \times 4 \times 8\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 96\)

$\blacksquare$