Divisor Sum of 285,778

Example of Divisor Sum of Square-Free Integer

$\map {\sigma_1} {285 \, 778} = 438 \, 768$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$285 \, 778 = 2 \times 43 \times 3323$

Hence:

\(\ds \map {\sigma_1} {285 \, 778}\)

\(=\)

\(\ds \paren {2 + 1} \times \paren {43 + 1} \times \paren {3323 + 1}\)

Divisor Sum of Square-Free Integer

\(\ds \)

\(=\)

\(\ds 3 \times 44 \times 3324\)

\(\ds \)

\(=\)

\(\ds 3 \times \paren {2^2 \times 11} \times \paren {2^2 \times 3 \times 277}\)

\(\ds \)

\(=\)

\(\ds 2^4 \times 3^2 \times 11 \times 277\)

\(\ds \)

\(=\)

\(\ds 438 \, 768\)

$\blacksquare$