On the largest prime divisor of an odd harmonic number

DOI10.1090/S0025-5718-07-01933-3zbMath1151.11008OpenAlexW1997323808WikidataQ114093880 ScholiaQ114093880MaRDI QIDQ3433771

Takeshi Goto, Yasuo Ohno, Yusuke Chishiki

Publication date: 2 May 2007

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-07-01933-3

zbMATH Keywords

perfect numbersharmonic numbers

Mathematics Subject Classification ID

Arithmetic functions; related numbers; inversion formulas (11A25) Values of arithmetic functions; tables (11Y70)

Related Items

Odd perfect numbers have a prime factor exceeding $10^8$ ⋮ Computers as a novel mathematical reality. III: Mersenne numbers and sums of divisors

Cites Work

• Über das harmonische Mittel der Teiler einer natürlichen Zahl. I, II
• Upper bounds for unitary perfect numbers and unitary harmonic numbers
• Numbers whose positive divisors have small integral harmonic mean
• The Second Largest Prime Factor of an Odd Perfect Number
• On the Largest Prime Divisor of an Odd Perfect Number. II
• The second largest prime divisor of an odd perfect number exceeds ten thousand
• Every odd perfect number has a prime factor which exceeds 10⁶
• All numbers whose positive divisors have integral harmonic mean up to $\mathbf {300}$
• Odd perfect numbers have a prime factor exceeding $10^{7}$
• The third largest prime divisor of an odd perfect number exceeds one hundred
• On the Largest Prime Divisor of an Odd Perfect Number
• On the Averages of the Divisors of a Number
• On Numbers with Integral Harmonic Mean
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