Divisor Sum of 1034

Example of Divisor Sum of Square-Free Integer

$\map {\sigma_1} {1034} = 1728$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$1034 = 2 \times 11 \times 47$

Hence:

\(\ds \map {\sigma_1} {994}\)

\(=\)

\(\ds \paren {2 + 1} \paren {11 + 1} \paren {47 + 1}\)

Divisor Sum of Square-Free Integer

\(\ds \)

\(=\)

\(\ds 3 \times 12 \times 48\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 2^6 \times 3^3\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 1728\)

$\blacksquare$