Divisor Sum of 945

Example of Divisor Sum of Integer

$\map {\sigma_1} {945} = 1920$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$945 = 3^3 \times 5 \times 7$

Hence:

\(\ds \map {\sigma_1} {945}\)

\(=\)

\(\ds \dfrac {3^4 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {7 + 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds 40 \times 6 \times 8\)

\(\ds \)

\(=\)

\(\ds \paren {2^3 \times 5} \times \paren {2 \times 3} \times 2^3\)

\(\ds \)

\(=\)

\(\ds 2^7 \times 3 \times 5\)

\(\ds \)

\(=\)

\(\ds 1920\)

$\blacksquare$