Divisor Sum of 286

Example of Divisor Sum of Square-Free Integer

$\map {\sigma_1} {286} = 504$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$286 = 2 \times 11 \times 13$

Hence:

\(\ds \map {\sigma_1} {286}\)

\(=\)

\(\ds \paren {2 + 1} \paren {11 + 1} \paren {13 + 1}\)

Divisor Sum of Square-Free Integer

\(\ds \)

\(=\)

\(\ds 3 \times 12 \times 14\)

\(\ds \)

\(=\)

\(\ds 3 \times \paren {2^2 \times 3} \times \paren {2 \times 7}\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 504\)

$\blacksquare$