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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 405.10036

**Autor: ** Erdös, Paul; Odlyzko, Andrew M.

**Title: ** On the density of odd integers of the form (p-1)2^{-n} and related questions. (In English)

**Source: ** J. Number Theory 11, 257-263 (1979).

**Review: ** Given k primes p_{1},...,p_{k}, write p-1 = p_{1}^{a1}... p_{k}^{ak}s_{p}, where s_{p} is coprime to P = p_{1}p_{2}... p_{k}. It is proved that the sequence of numbers occuring as s_{p} for some prime p has positive lower density. The most interesting unsolved problem is whether this sequence (s_{p}) can contain all numbers, coprime to P; concerning this question some numerical data are given.

**Reviewer: ** I.Z.Ruzsa

**Classif.: ** * 11B83 Special sequences of integers and polynomials

11N05 Distribution of primes

11N35 Sieves

**Keywords: ** primes of special form; divisors; sieve methods; density

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