Divisor Sum of 195

Example of Divisor Sum of Integer

$\map {\sigma_1} {195} = 336$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$195 = 3 \times 5 \times 13$

Hence:

\(\ds \map {\sigma_1} {195}\)

\(=\)

\(\ds \paren {3 + 1} \paren {5 + 1} \paren {13 + 1}\)

Divisor Sum of Square-Free Integer

\(\ds \)

\(=\)

\(\ds 4 \times 6 \times 14\)

\(\ds \)

\(=\)

\(\ds 2^2 \times \paren {2 \times 3} \times \paren {2 \times 7}\)

\(\ds \)

\(=\)

\(\ds 2^4 \times 3 \times 7\)

\(\ds \)

\(=\)

\(\ds 336\)

$\blacksquare$