A New Classification of Positive Integers Via New Divisor Functions

2025/09/07 by Brahim Mittou, Mittou, Brahim
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #General Mathematics (math.GM) #Iterative Methods for Nonlinear Equations #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2509.08844

openalex publication_date 2025/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let d₁ = 1 < d₂ < d₃ < ⋯ < d_τ(n) = n denote the increasing sequence of the divisors of a positive integer n. In this paper, for real or complex values of α, we define and study some properties of two new divisor functions σ_e,α and σ_o,α. The first computes the sum of the α-th powers of the divisors of n with even indices, and the second computes the sum of the α-th powers of the divisors of n with odd indices. We also introduce a new type of positive integers, namely, k-index ratio numbers and state three conjectures related to them.

Citations

• On Zumkeller Numbers

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