Function that enumerates a recursively enumerable language
This function maps nonnegative integers to the set of integers of the form $a^pb^p$. Enumerating is trivial, just start $i$ from 0, compute $p_{i+1}$-th prime, compute $a^{p_{i+1}}b^{p_{i+1}}$ and output that number. 

As for the index $i+1$, I guess that is because $0 \in N$ and it is assumed that primes are ordered starting from the index 1 not from 0, in other words we start from $p_1$ not from $p_0$, e.g., $f(0) = a^{p_1}b^{p_1}$.