Divisor Sum of 102

Example of Divisor Sum of Square-Free Integer

$\map {\sigma_1} {102} = 216$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$102 = 2 \times 3 \times 17$

Hence:

\(\ds \map {\sigma_1} {102}\)

\(=\)

\(\ds \paren {2 + 1} \paren {3 + 1} \paren {17 + 1}\)

Divisor Sum of Square-Free Integer

\(\ds \)

\(=\)

\(\ds 3 \times 4 \times 18\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 216\)

$\blacksquare$