Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-25T15:41:29.732Z Has data issue: false hasContentIssue false
  • English
  • Français

On a theorem of Behrend

Published online by Cambridge University Press:  09 April 2009

P. Erdös ,
A. Sárközy  and
E. Szemerédi
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A sequence of integers 0 <a1 < a2 <… no term of which divides any other will be called a primitive sequence. Throughout this paper c1, c2,… will denote suitable positive absolute constants. Behrend [1] proved that for every primitive sequence

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 1 , February 1967 , pp. 9 - 16
Copyright
Copyright © Australian Mathematical Society 1967

References

[1]Behrend, F., ‘On sequences of numbers not divisible one by another’, J. London Math. Soc. 10 (1935), 42–45.CrossRefGoogle Scholar
[2]de Bruijn, N. G., ‘On the number of uncancelled elements in the sieve of Eratosthenes’, Indagationes Math. 12 (1950) 247–256.Google Scholar
[3]Erdös, P., ‘On the integers having exactly κ prime factors’, Annals of Math. 49 (1948), 53–66.Google Scholar
[4]Erdös, P., ‘Note on sequences of integers no one of which is divisible by any other’, J. London Math. Soc. 10 (1935), 126–128.Google Scholar
[5]Sperner, E., ‘Ein Satz über Untermengen einer endlichea Menge’, Math. Zeitschrift 27 (1928), 544–548.CrossRefGoogle Scholar