Divisor Sum of 748

Example of Divisor Sum of Integer

$\map {\sigma_1} {748} = 1512$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$748 = 2^2 \times 11 \times 17$

Hence:

\(\ds \map {\sigma_1} {748}\)

\(=\)

\(\ds \frac {2^3 - 1} {2 - 1} \times \paren {11 + 1} \times \paren {17 + 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds 7 \times 12 \times 18\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 1512\)

$\blacksquare$