Divisor Sum of 22,976

Example of Divisor Sum of Integer

$\map {\sigma_1} {22 \, 976} = 45 \, 720$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$22 \, 976 = 2^6 \times 359$

Hence:

\(\ds \map {\sigma_1} {22 \, 976}\)

\(=\)

\(\ds \frac {2^7 - 1} {2 - 1} \times \paren {359 + 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds 127 \times 360\)

\(\ds \)

\(=\)

\(\ds 127 \times \paren {2^3 \times 3^2 \times 5}\)

\(\ds \)

\(=\)

\(\ds 2^3 \times 3^2 \times 5 \times 127\)

\(\ds \)

\(=\)

\(\ds 45 \, 720\)

$\blacksquare$