Levely Multiplicative Functions on N

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.