On near-perfect numbers of special forms
Elchin Hasanalizade
TL;DR
This paper explores the existence and properties of near-perfect numbers across different special forms, including Fibonacci, Lucas sequences, polynomial values, and repdigit numbers, expanding understanding of near-perfect number distribution.
Contribution
It introduces new results on the occurrence of near-perfect numbers within Fibonacci, Lucas sequences, polynomial outputs, and repdigit numbers, highlighting their special forms.
Findings
Near-perfect numbers exist in Fibonacci and Lucas sequences.
Certain polynomial values are identified as near-perfect numbers.
Examples of repdigit near-perfect numbers are provided.
Abstract
In this paper we discuss near-perfect numbers of various forms. In particular, we study the existence of near-perfect numbers in the Fibonacci and Lucas sequences, near-perfect values taken by integer polynomials and repdigit near-perfect numbers.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Computability, Logic, AI Algorithms · Benford’s Law and Fraud Detection