Characterizing Quasi-Friendly Divisors
C. A. Holdener
Grinnell, IA 50112
J. A. Holdener
Department of Mathematics and Statistics
Gambier, OH 43022
Abundancy ratios are rational numbers k satisfying
σ(N)/N = k/m
for some N ∈ Z≥1, where σ
is the sum-of-divisors function. In this paper we examine abundancy ratios
of the form σ(m)+1 , where gcd(m, σ(m)
+ 1) = 1. Defining D to be a quasi-friendly divisor of N if
σ(N) = σ(D)+1 with D|N, our
main results characterize all possible quasi-friendly divisors D
having two or more distinct prime divisors and satisfying gcd(D,
σ(D) + 1) = 1. In fact, we prove that no such quasi-friendly
divisor can have more than two distinct prime divisors.
Full version: pdf,
(Concerned with sequences
Received May 25 2020;
revised versions received August 14 2020; August 22 2020.
Published in Journal of Integer Sequences,
September 2 2020.
Journal of Integer Sequences home page