Divisor Sum of 272

Example of Divisor Sum of Integer

$\map {\sigma_1} {272} = 558$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$272 = 2^4 \times 17$

Hence:

\(\ds \map {\sigma_1} {272}\)

\(=\)

\(\ds \frac {2^5 - 1} {2 - 1} \times \frac {17^2 - 1} {17 - 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds \frac {31 - 1} 1 \times \frac {289 - 1} {16}\)

\(\ds \)

\(=\)

\(\ds 31 \times 18\)

\(\ds \)

\(=\)

\(\ds \paren {2 \times 3^2} \times 31\)

\(\ds \)

\(=\)

\(\ds 558\)

$\blacksquare$