Divisor Sum of 4030

Example of Divisor Sum of Square-Free Integer

$\map {\sigma_1} {4030} = 8064$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$4030 = 2 \times 5 \times 13 \times 31$

Hence:

\(\ds \map {\sigma_1} {4030}\)

\(=\)

\(\ds \paren {2 + 1} \paren {5 + 1} \paren {13 + 1} \paren {31 + 1}\)

Divisor Sum of Square-Free Integer

\(\ds \)

\(=\)

\(\ds 3 \times 6 \times 14 \times 32\)

\(\ds \)

\(=\)

\(\ds 3 \times \paren {2 \times 3} \times \paren {2 \times 7} \times 2^5\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 8064\)

$\blacksquare$