Divisor Sum of Power of Prime/Examples/81
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Example of Divisor Sum of Power of Prime
- $\map {\sigma_1} {81} = 121$
where $\sigma_1$ denotes the divisor sum function.
Proof
From Divisor Sum of Power of Prime:
- $\map {\sigma_1} {p^k} = \dfrac {p^{k + 1} - 1} {p_i - 1}$
We have that:
- $81 = 3^4$
Hence:
\(\ds \map {\sigma_1} {81}\) | \(=\) | \(\ds \frac {3^5 - 1} {2 - 1}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \frac {242} 2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 121\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 11^2\) |
$\blacksquare$