Affiliation:
1. Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China
Abstract
In this paper, we introduce the concept of F-perfect number, which is a positive integer n such that ∑d|n,d<n d2 = 3n. We prove that all the F-perfect numbers are of the form n = F2k-1 F2k+1, where both F2k-1 and F2k+1 are Fibonacci primes. Moreover, we obtain other interesting results and raise a new conjecture on perfect numbers.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
2 articles.
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1. What’s Special about the Perfect Number 6?;The American Mathematical Monthly;2021-01-02
2. On even perfect numbers;Colloquium Mathematicum;2018