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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 10 | Year 2020 | Article Id. IJMTT-V66I10P520 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I10P520

Superperfect Numbers and Some Ideas


Kalpok Guha
Abstract

A positive integer n is called perfect number if σ(n) = 2n. In this paper we discuss few properties of perfect numbers and then extend the idea of perfect numbers to superperfect numbers. A positive integer n is said to be a superperfect number if σ(σ(n) = 2n. Then we study few properties of these superperfect numbers.

Keywords
Divisor Function, Mersenne Primes, Multiplicative Functions, Perfect Numbers, Superperfect Numbers.
References

[1] Suryanarayana, D .Superperfect numbers. elem. Math., vol. 24, pp. 213-225, 1969.
[2] Burton, D.M. 2002. Elementary number theory. Boston: McGraw-Hill.
[3] Kanold, H.-J. Uber Super perfect numbers. elem. math. 24, pp. 61-62, 1969.
[4] Ratzan, L. (1972). Comments on the Properties of Odd Perfect Numbers. Pi Mu Epsilon Journal, 5(6), 265-271.
[5] Bege, Antal and Fogarasi, Kinga. (2010). Generalized perfect numbers.
[6] Holdener, J. (2002). A Theorem of Touchard on the Form of Odd Perfect Numbers. The American Mathematical Monthly, 109(7), 661-663.
[7] Ochem, Pascal; Rao, Michael (2012). Odd perfect numbers are greater than 101500. Mathematics of Computation, 81 (279).
[8] Sylvester, James Joseph . Sur l'impossibilitie de l'existence d'un nombre parfait qui ne contient pas au 5 diviseurs premiers distincts. Comptes Rendus, vol CVI, (1888) pp 522{526.
[9] Pomerance,C . Odd perfect numbers are divisible by at least seven distinct primes. Acta Arith., 25 (1974), 265-300.

Citation :

Kalpok Guha, "Superperfect Numbers and Some Ideas," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 10, pp. 167-169, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I10P520

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