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On Exactly k-deficient-perfect Numbers.

On exactly \(k\)-deficient-perfect numbers
Authors: Chen, F.;

On Exactly k-deficient-perfect Numbers.

Abstract

Summary: For a positive integer \(n\), let \(\sigma(n)\) denote the sum of all positive divisors of \(n\). A positive integer \(n\) is called an exactly \(k\)-deficient-perfect number if \(\sigma(n) = 2n-d_1 - d_2 - \cdots d_k\), where \(d_i\) \((1 < i < k)\) are distinct proper divisors of \(n\). In this paper, we determine all odd exactly 2-deficient-perfect numbers \(n\) with two distinct prime divisors.

Keywords

Arithmetic functions; related numbers; inversion formulas

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