Displaying similar documents to “Infinite sets of integers whose distinct elements do not sum to a power.”

On a sum of divisors problem.

De Koninck, Jean-Marie, Ivić, Aleksandar (1998)

Publications de l'Institut Mathématique. Nouvelle Série

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On near-perfect and deficient-perfect numbers

Min Tang, Xiao-Zhi Ren, Meng Li (2013)

Colloquium Mathematicae

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For a positive integer n, let σ(n) denote the sum of the positive divisors of n. Let d be a proper divisor of n. We call n a near-perfect number if σ(n) = 2n + d, and a deficient-perfect number if σ(n) = 2n - d. We show that there is no odd near-perfect number with three distinct prime divisors and determine all deficient-perfect numbers with at most two distinct prime factors.