Changing the index of the given sum

Question

Calculate $f(i)$ from the following equation of sums:

$$\sum_{i=n^4}^{n^6}a_{(i+52)^7}=\sum_{i=n^3-70}^{n^9-70}a_{f(i)}$$

Using 1st and last limits of the sum we have, $f(n^3-70)=(n^4+52)^7$ and $f(n^9-70)=(n^6+52)^7$. I have no idea how to evaluate $f$ from these ! Any help please...

Answer 1

The first sum has $n^6-n^4+1$ terms.

The second sum has $n^9-n^3+1$ terms.

Without further information, such mapping doesn't exist.