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  Volume 6, Issue 2, Article 31
 
A Note On Sums Of Powers Which Have A Fixed Number Of Prime Factors
    Authors: Rafael Jakimczuk,  
    Keywords: Sums of powers, Numbers with $k$ prime factors.  
    Date Received: 05/10/04  
    Date Accepted: 16/02/05  
    Subject Codes:

11N25, 11N37.

  
    Editors: László Tóth,  
 
    Abstract:

Let us denote by $ c_{n,k}$ the sequence of numbers which have in its factorization $ k$ prime factors ($ kgeq 1)$, we obtain in short proofs asymptotic formulas for $ c_{n,k}$, $ sum_{i=1}^{n}{c_{i,k}^{alpha }}$ and $ sum_{c_{i,k} leq x}{c_{i,k}^{alpha }}$. We generalize the work by T. Sálat y S. Znam when $ k=1$ (see reference [2]).

         
       
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