Divisor Sum of 679

Example of Divisor Sum of Integer

$\map {\sigma_1} {679} = 784$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$679 = 7 \times 97$

Hence:

\(\ds \map {\sigma_1} {679}\)

\(=\)

\(\ds \paren {7 + 1} \paren {97 + 1}\)

Divisor Sum of Square-Free Integer

\(\ds \)

\(=\)

\(\ds 8 \times 98\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 2^4 \times 7^2\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 784\)

$\blacksquare$