Divisor Sum of Power of Prime/Examples/81

Example of Sigma Function of Power of Prime

 * $\map \sigma {81} = 121$

where $\sigma$ denotes the $\sigma$ function.

Proof
From Sigma Function of Power of Prime:
 * $\map \sigma {p^k} = \dfrac {p^{k + 1} - 1} {p_i - 1}$

We have that:
 * $81 = 3^4$

Hence: