On near-perfect numbers

DOI10.4064/aa180821-11-10zbMath1465.11036arXiv1610.04253OpenAlexW3013070287MaRDI QIDQ5896117

Chung Hang Kwan, Alyssa Epstein, Steven J. Miller, Katherine Cordwell, Peter Cohen, Adam Lott

Publication date: 16 July 2020

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.04253

zbMATH Keywords

asymptotic behaviorperfect numbersarithmetic functionssum of divisors functionnear-perfect numberspseudoperfect numbers

Mathematics Subject Classification ID

Special sequences and polynomials (11B83) Arithmetic functions; related numbers; inversion formulas (11A25) Distribution of integers with specified multiplicative constraints (11N25)

Related Items (2)

Generalizing Ruth-Aaron Numbers ⋮ Computers as a novel mathematical reality. III: Mersenne numbers and sums of divisors

Cites Work

• On perfect and near-perfect numbers
• On perfect and multiply perfect numbers
• Über die Verteilung der vollkommenen Zahlen und allgemeinerer Zahlenmengen
• Über die Häufigkeit vollkommener Zahlen
• The Brun-Hooley sieve
• ON NEAR-PERFECT NUMBERS WITH TWO DISTINCT PRIME FACTORS
• DIVISOR‐SUM FIBERS
• On composite n for which φ(n) | n -1
• On Weird and Pseudoperfect Numbers
• ON CONGRUENCES OF THE FORM σ(n) ≡ a (mod n)
• On the distribution of some integers related to perfect and amicable numbers
• Odd perfect numbers, Diophantine equations, and upper bounds
• On the congruences $σ(n) ≡ a (mod n)$ and $n ≡ a (mod φ(n))$
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