Divisor Sum of 88

Example of Divisor Sum of Integer

$\map {\sigma_1} {88} = 180$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$88 = 2^3 \times 11$

Hence:

\(\ds \map {\sigma_1} {88}\)

\(=\)

\(\ds \frac {2^4 - 1} {2 - 1} \times \frac {11^2 - 1} {11 - 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds \frac {16 - 1} 1 \times \frac {121 - 1} {10}\)

\(\ds \)

\(=\)

\(\ds 15 \times 12\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 180\)

$\blacksquare$