Odd perfect numbers

DOI10.1017/S0305004100072030zbMath0805.11005OpenAlexW1993078701WikidataQ56625316 ScholiaQ56625316MaRDI QIDQ4303434

D. R. Heath-Brown

Publication date: 5 February 1995

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004100072030

zbMATH Keywords

divisor functionodd multiply perfect numbers

Mathematics Subject Classification ID

Arithmetic functions; related numbers; inversion formulas (11A25)

Related Items (14)

Sieve methods for odd perfect numbers ⋮ On numbers \(n\) for which the prime factors of \(\sigma(n)\) are among the prime factors on \(n\) ⋮ Spoof odd perfect numbers ⋮ On the number of distinct prime factors of an odd perfect number ⋮ Computers as a novel mathematical reality. III: Mersenne numbers and sums of divisors ⋮ Perfect polynomials over \(\mathbb F_4\) with less than five prime factors ⋮ AN UPPER BOUND FOR THE NUMBER OF ODD MULTIPERFECT NUMBERS ⋮ Upper bounds for unitary perfect numbers and unitary harmonic numbers ⋮ IMPROVED UPPER BOUNDS FOR ODD MULTIPERFECT NUMBERS ⋮ NOTE ON ODD MULTIPERFECT NUMBERS ⋮ Odd perfect numbers have at least nine distinct prime factors ⋮ BOUNDS FOR ODD k-PERFECT NUMBERS ⋮ Odd perfect numbers, Diophantine equations, and upper bounds ⋮ ON ODD PERFECT NUMBERS

Cites Work

• Multiply perfect numbers, Mersenne primes, and effective computability
• Outline of a Proof that Every Odd Perfect Number has at Least Eight Prime Factors
• Improved Techniques for Lower Bounds for Odd Perfect Numbers

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