Divisor Sum of 2024

Example of Divisor Sum of Integer

$\map {\sigma_1} {2024} = 4320$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$2024 = 2^3 \times 11 \times 23$

Hence:

\(\ds \map {\sigma_1} {2024}\)

\(=\)

\(\ds \dfrac {2^4 - 1} {2 - 1} \times \paren {11 + 1} \times \paren {23 + 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds 15 \times 12 \times 24\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 4320\)

$\blacksquare$