On k-Hyperperfect and Super Hyperperfect
Numbers

V Puneeth

doi:https://doi.org/10.14445/22315373/IJMTT-V63P508

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 63 | Number 1 | Year 2018 | Article Id. IJMTT-V63P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V63P508

On k-Hyperperfect and Super Hyperperfect Numbers

V Puneeth

Abstract

A positive integer n is said to be a superperfect number, if 𝜎 𝜎 𝑛 = 2𝑛. k-hyperperfect number, if 𝜎 𝑛 = 𝑘+1 𝑘 𝑛 + 𝑘−1 𝑘 where the function 𝜎 𝑛 is the sum of all positive divisors of n. In this paper we investigate some general results on k-hyperperfect numbers and super hyperperfect numbers.

Keywords

Divisor function, Mersenne prime, Perfect number, Super perfect number, Hyperperfect number and super hyperperfect number .

References

[1] B.Das and H.K.Saikia, “Identities for near and deficient hyperperfect numbers,” Indian, J. Math. Soft Comput., vol. 3, pp. 214-134, 2016.
[2] D.Suryanarayana, “Superperfect numbers,” elem. Math., vol. 24, pp. 213-225, 1969.
[3] D.Manoli and R.Bear, “Hyperperfect numbers,” Pi Mu Epsilon J., vol. 6, pp. 153-157, 1975.
[4] V.Puneeth and T.V.Joseph, “On k-Near Perfect Numbers,” Int. J. Math. And. Appl., vol. 1, pp. 61-65, 2018.
[5] A.Bege and K.Fogarasi, “Generalised Perfect Numbers,” Acta Univ. Sapientiae. Mathematica., vol. 1, pp. 73-82, 2009.
[6] L.E.Dickenson, History of theory of numbers, vol 1, Newyork: Chelsea Publishing Co., 1966.

Citation :

V Puneeth, "On k-Hyperperfect and Super Hyperperfect Numbers," International Journal of Mathematics Trends and Technology (IJMTT), vol. 63, no. 1, pp. 65-67, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V63P508