# Partitions into perfect kth prime powers

I am trying to return partitions of $n$ into perfect $k$th powers of primes, call the function $pp^k(n)$ where $k$ is the $k$th power, so for instance $pp^2(24)=3$ since $24=2^2+2^2+2^2+2^2+2^2+2^2=3^2+3^2+2^2=4^2+2^2+2^2$. I have the code that returns prime partitions of $n$ but I cannot figure out how to tweak it to return perfect $k$th powers.

```
def pp(n):
return Partitions(n,parts_in=prime_range(n+1)).cardinality:
for n in srange(1,100):
print(n,pp(n))
```

Can someone please help. Thank you so much!

I'm confused: first, 3^2 + 3^2 + 2^2 is not 24, and second, 4 is not a prime, so 4^2 is not the square of a prime. Shouldn't pp^2(24) = 1?