*x*] be the digital root function (also known as the repeated digital sum function), where one adds the digits of positive integer

*x*, then adds the digits of the sum until obtaining a single-digit number. (For example, S[975] = 3 because 9 + 7 + 5 = 21 and 2 + 1 = 3).

Given S[

*a*

^{a}] = 2, what is the smallest positive integer that

**can be such that**

*a***is a perfect power?**

*a*Note:

*a*is a perfect power if there exist natural numbers m > 1, and k > 1 such that

*m*.

^{k}= a