Divisor Sum of 9374

Example of Divisor Sum of Square-Free Integer

$\map {\sigma_1} {9374} = 14 \, 520$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$9374 = 2 \times 43 \times 109$

Hence:

\(\ds \map {\sigma_1} {9374}\)

\(=\)

\(\ds \paren {2 + 1} \paren {43 + 1} \paren {109 + 1}\)

Divisor Sum of Square-Free Integer

\(\ds \)

\(=\)

\(\ds 3 \times 44 \times 110\)

\(\ds \)

\(=\)

\(\ds 3 \times \paren {2^2 \times 11} \times \paren {2 \times 5 \times 11}\)

\(\ds \)

\(=\)

\(\ds 2^3 \times 3 \times 5 \times 11^2\)

\(\ds \)

\(=\)

\(\ds 14 \, 520\)

$\blacksquare$