Year: 2025
Type: article
Abstract: Let k ≥ 2 be an integer and σ k (n) be the sum of the kth powers of the positive divisors of n.In this paper, we prove that if (Un) n≥1 is any nondegenerate linearly recurrent sequence of integers whose general term is up to sign not a polynomial in n, then the inequality σ k (|Un|) ≤ |U σ k (n) | holds for all n sufficiently large, and the inequality σ(for almost all natural numbers n, where σ(n) = σ1(n).In fact, the second inequality fails on a set of n ≤ x of counting function O(x/ log x).
Authors: Florian Luca, Makoko Campbell Manape
Institutions: Stellenbosch University, University of the Witwatersrand
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408908995