Divisor Sum of 710

Example of Divisor Sum of Integer

$\map {\sigma_1} {710} = 1296$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$710 = 2 \times 5 \times 71$

Hence:

\(\ds \map {\sigma_1} {710}\)

\(=\)

\(\ds \paren {2 + 1} \paren {5 + 1} \paren {71 + 1}\)

Divisor Sum of Square-Free Integer

\(\ds \)

\(=\)

\(\ds 3 \times 6 \times 72\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 1296\)

$\blacksquare$