Divisor Sum of 672

Example of Divisor Sum of Integer

$\map {\sigma_1} {672} = 2016$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$672 = 2^5 \times 3 \times 7$

Hence:

\(\ds \map {\sigma_1} {672}\)

\(=\)

\(\ds \frac {2^6 - 1} {2 - 1} \times \paren {3 + 1} \times \paren {7 + 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds \frac {63} 1 \times 4 \times 8\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 2^5 \times 3^2 \times 7\)

\(\ds \)

\(=\)

\(\ds 2016\)

$\blacksquare$