Multiply perfect numbers, Mersenne primes, and effective computability

DOI10.1007/BF01362422zbMath0324.10001MaRDI QIDQ1224593

Carl B. Pomerance

Publication date: 1977

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/162952

Mathematics Subject Classification ID

Arithmetic functions; related numbers; inversion formulas (11A25) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (13)

Sieve methods for odd perfect numbers ⋮ Outline of a Proof that Every Odd Perfect Number has at Least Eight Prime Factors ⋮ Odd perfect numbers ⋮ On the number of distinct prime factors of an odd perfect number ⋮ On Odd Perfect, Quasiperfect, and Odd Almost Perfect Numbers ⋮ Computers as a novel mathematical reality. III: Mersenne numbers and sums of divisors ⋮ On finiteness of odd superperfect numbers ⋮ AN UPPER BOUND FOR THE NUMBER OF ODD MULTIPERFECT NUMBERS ⋮ Upper bounds for unitary perfect numbers and unitary harmonic numbers ⋮ NOTE ON ODD MULTIPERFECT NUMBERS ⋮ Odd perfect numbers have at least nine distinct prime factors ⋮ A note on the paper by Bugeaud and Laurent ``Minoration effective de la distance \(p\)-adique entre puissances de nombres algébriques ⋮ BOUNDS FOR ODD k-PERFECT NUMBERS

Cites Work

• Unnamed Item
• Über einen Satz von L. E. Dickson. I, II
• Über die Häufigkeit vollkommener Zahlen
• Bemerkung zu der Arbeit über vollkommene Zahlen in Math. Ann. Bd. 133, S. 431-438 (1957)
• Ein Satz über natürliche Zahlen \(N\) mit \(\sigma(N)=3N\)
• On the problem of odd h-fold perfect numbers
• Eine Schranke für befreundete Zahlen mit gegebener Teileranzahl
• Advanced Problems: 5964-5869
• On primitive abundant numbers
• Linear forms in the logarithms of algebraic numbers (IV)
• Note on a theorem of Dickson

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