On the densities of sets of multiples

Mathematical Proceedings of the Cambridge Philosophical Society, 1992

Let denote a sequence of integers exceeding 1, and let τ(n, ) be the number of those divisors of n which belong to . We say that is a Behrend sequence ifwhere, here and in the sequel, we use the notation p.p. to indicate that a relation holds on a set of asymptotic density one.

Mathematical Proceedings of the Cambridge Philosophical Society, 1996

2004

A survey of recent results in elementary number theory is presented in this paper. Special attention is given to structure and asymptotic properties of certain families of positive integers.

Mathematica Slovaca, 2004

Properties of distribution functions of block sequences were investigated in [STRAUCH, O .—TOTH, J. T.: Distribution functions of ratio sequences, Publ . Math. Debrecen 58 (2001), 751-778]. The present paper is a continuation of the study of relations between the density of the block sequence and so called dispersion of the block sequence. Preliminaries In this part we recall some basic definitions. Denote by N and M the set of all positive integers and positive real numbers, respectively. For X C N let X(n) = card{x G X : x < n}. In the whole paper we will assume that X is infinite. Denote by R(X) = { | : x G X, y G X} the ratio set of X and say that a set X is (R) -dense if R(X) is (topologically) dense in the set M . Let us notice that the concept of (It)-density was defined and first studied in papers [SI] and [S2]. Now let X = {x1,x2,...} where xn < x n + 1 are positive integers. The following sequence of finite sequences derived from X X rp rp rp rp rp rp rp rv* (1) ^1 ^...

Mathematica Slovaca, 1997

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1996

2004

A survey of recent results in elementary number theory is presented in this paper. Special attention is given to structure and asymptotic properties of certain families of positive integers. In particular, a conjecture on complete sequences of Burr, Erdős, Graham and Wen-Ching Li is amended.

Uniform distribution theory, 2018

In Part I of this paper we studied the irregularities of distribution of binary sequences relative to short arithmetic progressions. First we introduced a quantitative measure for this property. Then we studied the typical and minimal values of this measure for binary sequences of a given length. In this paper our goal is to give constructive bounds for these minimal values.

Periodica Mathematica Hungarica, 2006

The periodicity of sequences of integers (an) n∈Z satisfying the inequalities 0 ≤ a n−1 + λan + a n+1 < 1 (n ∈ Z)

Mathematica Slovaca, 1993

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.