Niveau: Secondaire, Collège, TroisièmeDiscrete mathematics 200 (1999), 181-203. Ensembles de multiples de suites finies P. Erdo˝s & G. Tenenbaum Abstract. A Behrend sequence is a (necessarily infinite) integer sequence A with elements exceeding 1 and whose set of multiples M(A) has logarithmic density µ(A) = 1. By a famous theorem of Davenport and Erdo˝s, this implies that M(A) also has natural density equal to 1. An ?-pseudo-Behrend sequence is a finite sequence of integers exceeding 1 with µ(A) > 1 ? ?. We show that for any given ? ?]0, 1[ and any function ?N ?∞, the maximal number of disjoint ?-pseudo-Behrend sequences included in [1, N ] is (logN)log 2eO(?N √ log2 N). We also prove that, for any given positive real number ?, there is a positive constant c = c(?) such that c distribution function behrend behrend sequence e?n √ log2 entier limite donnee ?n ?
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