Divisor Sum of 742

Example of Divisor Sum of Integer

$\map {\sigma_1} {742} = 1296$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$742 = 2 \times 7 \times 53$

Hence:

\(\ds \map {\sigma_1} {742}\)

\(=\)

\(\ds \paren {2 + 1} \paren {7 + 1} \paren {53 + 1}\)

Divisor Sum of Square-Free Integer

\(\ds \)

\(=\)

\(\ds 3 \times 8 \times 54\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 1296\)

$\blacksquare$