The number $512$ is interesting because it is equal to the sum of its digits raised to some power: $5+1+2=8$, and $8^3=512$. Another example of a number with this property is $614656={28}^4$.

We shall define $a_n$ to be the $n$th term of this sequence and insist that a number must contain at least two digits to have a sum.

You are given that $a_2=512$ and $a_{10}=614656$.

Find $a_{30}$.