Divisor Sum of 78

Example of Divisor Sum of Square-Free Integer

$\map {\sigma_1} {78} = 168$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$78 = 2 \times 3 \times 13$

Hence:

\(\ds \map {\sigma_1} {78}\)

\(=\)

\(\ds \paren {2 + 1} \paren {3 + 1} \paren {13 + 1}\)

Divisor Sum of Square-Free Integer

\(\ds \)

\(=\)

\(\ds 3 \times 4 \times 14\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 168\)

$\blacksquare$