On perfect and near-perfect numbers
Vladimir Shevelev
TL;DR
This paper introduces the concept of near-perfect numbers, which are positive integers that are equal to the sum of all their proper divisors except one, and explores their properties and related theorems.
Contribution
It defines near-perfect numbers, proves an Euclid-like theorem for them, and presents new results on their properties.
Findings
Near-perfect numbers are characterized by a specific divisor sum property.
An Euclid-like theorem for near-perfect numbers is established.
Additional results on the structure and properties of near-perfect numbers are provided.
Abstract
We call positive integer n a near-perfect number, if it is sum of all its proper divisors, except of one of them ("redundant divisor"). We prove an Euclid-like theorem for near-perfect numbers and obtain some other results for them.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Advanced Mathematical Theories · Analytic Number Theory Research