The second largest prime divisor of an odd perfect number exceeds ten thousand
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Publication:4257704
DOI10.1090/S0025-5718-99-01126-6zbMath0927.11002WikidataQ56059207 ScholiaQ56059207MaRDI QIDQ4257704
Publication date: 31 August 1999
Published in: Mathematics of Computation (Search for Journal in Brave)
Arithmetic functions; related numbers; inversion formulas (11A25) Values of arithmetic functions; tables (11Y70)
Related Items (10)
Sieve methods for odd perfect numbers ⋮ Odd perfect numbers have a prime factor exceeding $10^{7}$ ⋮ On the number of distinct prime factors of an odd perfect number ⋮ Odd perfect numbers have a prime factor exceeding $10^8$ ⋮ Computers as a novel mathematical reality. III: Mersenne numbers and sums of divisors ⋮ Odd perfect numbers have at least nine distinct prime factors ⋮ The third largest prime divisor of an odd perfect number exceeds one hundred ⋮ Upper bounds on the second largest prime factor of an odd perfect number ⋮ On the largest prime divisor of an odd harmonic number ⋮ Odd perfect numbers, Diophantine equations, and upper bounds
Cites Work
- On distinguishing prime numbers from composite numbers
- Verschärfung der notwendigen Bedingungen für die Existenz von ungeraden vollkommenen Zahlen
- Non-existence of odd perfect numbers of the form \(3^{2\beta}p_1^{2\beta_1}s_2^{2\beta_2}s_3^{2\beta_3}\)
- Outline of a Proof that Every Odd Perfect Number has at Least Eight Prime Factors
- Improved Techniques for Lower Bounds for Odd Perfect Numbers
- The Second Largest Prime Factor of an Odd Perfect Number
- On the Largest Prime Divisor of an Odd Perfect Number. II
- Every odd perfect number has a prime factor which exceeds 10⁶
- On the Largest Prime Divisor of an Odd Perfect Number
- Odd perfect numbers are divisible by at least seven distinct primes
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