Raghavendra Bhat, Sundarraman Madhusudanan
Published 2022-11-04Version 1
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.
Comments: This paper is currently undergoing peer review
A generalization of a theorem of Boyd and Lawton
A generalization of the duality for multiple harmonic sums
Another generalization of a theorem of Baker and Davenport
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