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Generalized perfect numbers. (English) Zbl 1192.11003

A positive integer \(n\) is said to be superperfect if \(\sigma^2(n)=\sigma(\sigma(n))=2n\) and \(k\)-hyperperfect if \(\sigma(n)=\frac{k+1}{k}n+\frac{k-1}{k}\). The authors present some results and conjectures on hyperperfect and super-hyperperfect numbers. For a general account of perfect and related numbers, see J. Sándor and B. Crstici [Handbook of number theory. II. Dordrecht: Kluwer Academic Publishers (2004; Zbl 1079.11001)].

MSC:

11A25 Arithmetic functions; related numbers; inversion formulas
11Y70 Values of arithmetic functions; tables

Citations:

Zbl 1079.11001
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