Divisor Sum of 2025

Example of Divisor Sum of Integer

$\map {\sigma_1} {2025} = 7502$

where $\sigma_1$ denotes the divisor sum function.


Proof

We have that:

$2025 = 3^4 \times 5^2$

Hence:

\(\ds \map {\sigma_1} {2025}\) \(=\) \(\ds \frac {3^5 - 1} {3 - 1} \times \frac {5^3 - 1} {5 - 1}\) Divisor Sum of Integer
\(\ds \) \(=\) \(\ds 242 \times 31\)
\(\ds \) \(=\) \(\ds 2 \times 11^2 \times 31\)
\(\ds \) \(=\) \(\ds 7502\)

$\blacksquare$

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