Let $p$ be a prime number and $f(p)$ be the number of representations $$p=a+b$$ with perfect powers $0<a< b$
For example, $13$ has the only representation $$4+9=13$$ hence $f(13)=1$ $$41=9+32=16+25$$ has two representations, hence $f(41)=2$
The smallest primes that satisfy $$f(p)=1,2,3,4,5$$ are $$13,41,449,4481,93241$$ respective. I did not find this sequence in OEIS.
Is $f(p)$ a bounded function ? If not, is $f(p)$ surjective on the natural numbers ?