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Title

Maximal sets of numbers not containing k+1 pairwise coprime integers

Authors 1, 1

Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, Postfach 100 131, 33501 Bielefeld, Germany

Bibliography

  1. R. Ahlswede and L. H. Khachatrian, On extremal sets without coprimes, Acta Arith. 66 (1994), 89-99.
  2. N. G. de Bruijn, On the number of uncancelled elements in the sieve of Eratosthenes, Indag. Math. 12 (1950), 247-256.
  3. A. A. Buchstab, Asymptotische Abschätzungen einer allgemeinen zahlentheoretischen Funktion, Mat. Sb. (N.S.) 44 (1937), 1239-1246.
  4. P. Erdős, On the density of some sequences of integers, Bull. Amer. Math. Soc. 54 (1948), 685-692.
  5. P. Erdős, Remarks in number theory IV, Mat. Lapok 13 (1962), 228-255.
  6. P. Erdős, Extremal problems in number theory, in: Theory of Numbers, Proc. Sympos. Pure Math. 8, Amer. Math. Soc., Providence, R.I., 1965, 181-189.
  7. P. Erdős, Problems and results on combinatorial number theory, Chapt. 12 in: A Survey of Combinatorial Theory, J. N. Srivastava et al. (eds.), North-Holland, 1973.
  8. P. Erdős, A survey of problems in combinatorial number theory, Ann. Discrete Math. 6 (1980), 89-115.
  9. P. Erdős and A. Sárközy, On sets of coprime integers in intervals, Hardy-Ramanujan J. 16 (1993), 1-20.
  10. P. Erdős, A. Sárközy and E. Szemerédi, On some extremal properties of sequences of integers, Ann. Univ. Sci. Budapest. Eötvös 12 (1969), 131-135.
  11. P. Erdős, A. Sárközy and E. Szemerédi, On some extremal properties of sequences of integers, II, Publ. Math. Debrecen 27 (1980), 117-125.
  12. R. Freud, Paul Erdős, 80-A Personal Account, Period. Math. Hungar. 26 (2) (1993), 87-93.
  13. H. Halberstam and K. F. Roth, Sequences, Oxford University Press, 1966, Springer, 1983.
  14. R. R. Hall and G. Tenenbaum, Divisors, Cambridge Tracts in Math. 90, 1988.
  15. C. Szabó and G. Tóth, Maximal sequences not containing 4 pairwise coprime integers, Mat. Lapok 32 (1985), 253-257 (in Hungarian)
Acta Arithmetica
1995/72/1
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Pages:
77-100
Main language of publication
English
Received
1994-08-26
Accepted
1994-11-15
Published
1995
Exact and natural sciences