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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.41 no.3 Antofagasta June 2022 


Near-Zumkeller numbers

1 Department of Mathematics, Gauhati University, Guwahati-781014, India. e-mail:

2 Department of Mathematics, Gauhati University, Guwahati-781014, India. e-mail:


A positive integer n is called a Zumkeller number if the set of all the positive divisors of n can be partitioned into two disjoint subsets, each summing to σ(n)/2. In this paper, Generalizing further, near-Zumkeller numbers and k-near-Zumkeller numbers are defined and also some results concerning these numbers are established. Relations of these numbers with practical numbers are also studied in this paper.

Keywords: perfect numbers; Zumkeller numbers; practical numbers; fermat primes

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Received: January 30, 2021; Accepted: November 30, 2021

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License