On the Composition of the Functions and on the Set Zs(P)

Abstract

In this paper we dene the composition of σ and functions on the setIn this paper we dene the composition of σ and functions on the setZs(P), where is Dedekind's function and P = {p ∈ P; p = 2αk − 1, α ≥1, k > 1, (k, 2) = 1}, where P be the set of all odd primes and Zs(P) = {n =kj=1pj ; pj = 2αjmj − 1; αj ≥ 1,mj > 1, pj ∈ P}, where (mj ,mk) = 1 for allj ̸= k; j, k = 1, 2, . . . , r and prove that σ( (n))n≥ 1, for n ∈ Zs(P).