Some characterizations on odd deficient-perfect numbers

Journal of Lanzhou University of Technology ›› 2024, Vol. 50 ›› Issue (1): 158-167.

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Some characterizations on odd deficient-perfect numbers

ZHANG Si-bao^1,2

1. School of Mathematics and Statistics, Kashi University, Kashi 844000, China;
2. Research Center of Modern Mathematics and Its Application, Kashi University, Kashi 844000, China

Received:2022-08-31 Online:2024-02-28 Published:2024-03-04

Abstract

Abstract: In order to study the existence of odd-deficient perfect numbers with five different prime factors, the problem whether odd positive integer n with five different prime factors satisfy the definition of the odd deficient perfect number is discussed by using the elementary method. Several conclusions indicating that there are three classes of odd positive integers n with five different prime factors are not odd deficient perfect number.

Key words: deficient-perfect number, odd deficient perfect number, existence, arithmetical function

CLC Number:

O156

ZHANG Si-bao. Some characterizations on odd deficient-perfect numbers[J]. Journal of Lanzhou University of Technology, 2024, 50(1): 158-167.

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Some characterizations on odd deficient-perfect numbers

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