Divisor Sum of 572

Example of Divisor Sum of Integer

$\map {\sigma_1} {572} = 1176$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$572 = 2^2 \times 11 \times 13$

Hence:

\(\ds \map {\sigma_1} {572}\)

\(=\)

\(\ds \frac {2^3 - 1} {2 - 1} \times \paren {11 + 1} \times \paren {13 + 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds \frac {7 - 1} 1 \times 12 \times 14\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 1176\)

$\blacksquare$