  We defined numbers of the form $p\cdot a^2$ as SP numbers (Square-Prime
numbers) ($a\neq1$, $p$ prime) in the paper 'Distribution of Square-Prime
numbers' (arXiv:2109.10238) along with proofs on their distribution. Some
examples of SP Numbers : 75 = 3 $\cdot$ 25; 108 = 3 $\cdot$ 36; 45 = 5 $\cdot$
9. These numbers are listed in the OEIS as A228056. In this paper, we will
prove a few algebraic theorems and generalize the definition of SP Numbers to
allow factors of arbitrary natural number powers.
