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Levely Multiplicative Functions on N
Mathematicl Department, Faculty of Science, Gharyan University, Gharyan, Libya
Higher Institute of Engineering Technology, Zliten, Libya
- 1 Mathematicl Department, Faculty of Science, Gharyan University, Gharyan, Libya
- 2 Higher Institute of Engineering Technology, Zliten, Libya
Advances in Pure Mathematics·Volume 15 (2025)·Pages 643–650·Published 1 September 2025·DOI10.4236/apm.2025.159033
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Abstract
In this paper, as a result of dividing the set of natural numbers into disjoint levels, we have studied levely multiplicative functions that are defined from N to N and which keep numbers at the same level when restricted on levels, i.e. f | L i : L i → L i . We have defined the level multiplicative function and explained how to generate it using the restriction function f | L 1 . Furthermore, if f | L 1 is bijective, then all f | L i and f are bijective functions. Moreover, the levely multiplicative function preserves the unique factorization for any number n ∈ N and maintains divisibility properties.
KeywordsPrime-Power DecompositionLevels ofUpward Closed SetLevely Multiplicative Function
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