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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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