## Articulo

• Similares en SciELO

## versión impresa ISSN 0716-0917

### Proyecciones (Antofagasta) vol.41 no.3 Antofagasta jun. 2022

#### http://dx.doi.org/10.22199/issn.0717-6279-4320

Artículos

Near-Zumkeller numbers

1 Department of Mathematics, Gauhati University, Guwahati-781014, India. e-mail: harishp956@gmail.com

2 Department of Mathematics, Gauhati University, Guwahati-781014, India. e-mail: hsaikia@yahoo.com

Abstract

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

References

[1] D. Bhabesh and Helen K. Saikia, “Some Aspects of Certain Form of Near Perfect Numbers”, International Journal of Discrete Mathematics, vol. 2, no. 3, pp. 64-67, 2017. [ Links ]

[2] D. M. Burton, Elementary number theory. New Delhi: McGraw Hill Education, 2012. [ Links ]

[3] P. J. Mahanta, M. P. Saikia, and D. Yaqubi, “Some properties of Zumkeller numbers and K-layered numbers”, Journal of Number Theory, vol. 217, pp. 218-236, 2020. doi: 10.1016/j.jnt.2020.05.003 [ Links ]

[4] S. Clark, J. Dalzell, J. Holliday, D. Leach, M. Liatti, and M. Walsh, “Zumkeller numbers”, Mathematical Abundance Conference at Illinois State University, April 18th, 2018. [ Links ]

[5] Y. Peng and K. P. S. Bhaskara Rao, “On zumkeller numbers”, Journal of Number Theory , vol. 133, no. 4, pp. 1135-1155, 2013. doi: 10.1016/j.jnt.2012.09.020 [ Links ]

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