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!
