Algebraic Results on SP Numbers along with a generalization
Abstract
We defined numbers of the form p· a2 as SP numbers (Square-Prime numbers) (a≠1, 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 · 25; 108 = 3 · 36; 45 = 5 · 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.
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