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On the density of odd integers of the form $$(p-1)2^{-n}$$ and related questions. (English) Zbl 0405.10036
Given $$k$$ primes $$p_1,\dots,p_k$$, write $$p-1=p_1^{a_1}\dots p_k^{a_k}s_p$$, where $$s_p$$ is coprime to $$P=p_1p_2\dots p_k$$. It is proved that the sequence of numbers occurring 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.

##### MSC:
 11B05 Density, gaps, topology 11N05 Distribution of primes 11N35 Sieves
##### Keywords:
primes of special form; divisors; sieve methods; density
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##### References:
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