Divisor Sum of 22,744

Example of Divisor Sum of Integer

$\map {\sigma_1} {22 \, 744} = 42 \, 660$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$22 \, 744 = 2^3 \times 2843$

Hence:

\(\ds \map {\sigma_1} {22 \, 744}\)

\(=\)

\(\ds \frac {2^4 - 1} {2 - 1} \times \paren {2843 + 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds 15 \times 2844\)

\(\ds \)

\(=\)

\(\ds \paren {3 \times 5} \times \paren {2^2 \times 3^2 \times 79}\)

\(\ds \)

\(=\)

\(\ds 2^2 \times 3^3 \times 5 \times 79\)

\(\ds \)

\(=\)

\(\ds 42 \, 660\)

$\blacksquare$