On some estimates involving the number of prime divisors of an integer
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چکیده
منابع مشابه
On the Residue Class Distribution of the Number of Prime Divisors of an Integer
The Liouville function is defined by λ(n) := (−1)Ω(n) where Ω(n) is the number of prime divisors of n counting multiplicity. Let ζm := e2πi/m be a primitive m–th root of unity. As a generalization of Liouville’s function, we study the functions λm,k(n) := ζ kΩ(n) m . Using properties of these functions, we give a weak equidistribution result for Ω(n) among residue classes. More formally, we sho...
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Prime divisors of some shifted products
We study prime divisors of various sequences of positive integers A(n) + 1, n = 1,...,N, such that the ratios a(n) = A(n)/A(n − 1) have some number-theoretic or combinatorial meaning. In the case a(n) = n, we obviously have A(n) = n!, for which several new results about prime divisors of n! + 1 have recently been obtained.
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1987
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-49-1-21-33