Divisor Sum of Power of Prime/Examples/81

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: