On perfect and near-perfect numbers

DOI10.1016/j.jnt.2012.06.008zbMath1272.11013arXiv1011.6160OpenAlexW2025229782MaRDI QIDQ455810

Vladimir Shevelev, Paul Pollack

Publication date: 22 October 2012

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.6160

zbMATH Keywords

perfect numberpseudoperfect numbersum-of-divisors function

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 (11)

Unnamed Item ⋮ ON DEFICIENT-PERFECT NUMBERS ⋮ Unnamed Item ⋮ ON NEAR-PERFECT NUMBERS OF SPECIAL FORMS ⋮ Computers as a novel mathematical reality. III: Mersenne numbers and sums of divisors ⋮ Unnamed Item ⋮ ON CONGRUENCES OF THE FORM σ(n) ≡ a (mod n) ⋮ On near-perfect numbers ⋮ On even perfect numbers ⋮ Deficient perfect numbers with four distinct prime factors ⋮ ON NEAR-PERFECT NUMBERS WITH TWO DISTINCT PRIME FACTORS

Uses Software

• OEIS

Cites Work

• On the greatest common divisor of a number and its sum of divisors
• Über die Häufigkeit vollkommener Zahlen
• Bemerkung zu der Arbeit über vollkommene Zahlen in Math. Ann. Bd. 133, S. 431-438 (1957)
• On powers associated with Sierpiński numbers, Riesel numbers and Polignac's conjecture
• Primes with an average sum of digits
• On composite n for which φ(n) | n -1
• ON CONGRUENCES OF THE FORM σ(n) ≡ a (mod n)
• On the congruences $σ(n) ≡ a (mod n)$ and $n ≡ a (mod φ(n))$
• Unsolved problems in number theory
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