On near-perfect numbers with five prime factors

Title

On near-perfect numbers with five prime factors

Creator

Jeba F.S.; Roy A.; Saikia M.P.

Description

Let n be a positive integer and ?(n) the sum of all the positive divisors of n. We call n a near-perfect number with redundant divisor d if ?(n) = 2n + d. Let n be an odd near-perfect number of the form n = pa11 ? pa22 ? pa33 ? pa44 ? pa55 where pis are odd primes and ais (1 ? i ? 5) are positive integers. In this article, we prove that 3 | n and one of 5, 7, 11 | n. We also show that there exists no odd near-perfect number when n = 3a1 ? 7a2 ? pa33 ? pa44 ? pa55 with p3 ? {17, 19} and when n = 3a1 ? 11a2 ? pa33 ? pa44 ? pa55 Mathematical and Computational Sciences - Proceedings of the ICRTMPCS International Conference 2023.All rights reserved.

Source

De Gruyter Proceedings in Mathematics, pp. 207-220.

Date

2024-01-01

Publisher

Walter de Gruyter GmbH

Subject

divisor sum function; Near-perfect numbers; perfect numbers

Coverage

Jeba F.S., Department of Mathematics, CHRIST (Deemed to be University), Kanmanike, Kumbalgodu, Mysore Road, Karnataka, Bengaluru, 560074, India; Roy A., Department of Sciences and Humanities, CHRIST (Deemed to be University), Kanmanike, Kumbalgodu, Mysore Road, Karnataka, Bengaluru, 560074, India; Saikia M.P., Mathematical and Physical Sciences division, School of Arts and Sciences, Ahmedabad University, Commerce Six Roads, Navrangpura, Gujarat, Ahmedabad, 380009, India

Rights

Restricted Access

Relation

ISSN: 29424801; ISBN: 978-311130437-3

Format

Online

Language

English

Type

Conference paper

Identifier

https://doi.org/10.1515/9783111313634-016

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