JIPAM

Properties of Non Powerful Numbers  
 
  Authors: Vlad Copil, Laurentiu Panaitopol,  
  Keywords: Powerful numbers, Sequences, Inequalities, Goldbach's conjecture.  
  Date Received: 11/01/2008  
  Date Accepted: 10/03/2008  
  Subject Codes:

11B83, 11P32, 26D07.

  
  Editors: László Tóth,  
 
  Abstract:

In this paper we study some properties of non powerful numbers. We evaluate the $ n$-th non powerful number and prove for the sequence of non powerful numbers some theorems that are related to the sequence of primes: Landau, Mandl, Scherk. Related to the conjecture of Goldbach, we prove that every positive integer $ ge3$ is the sum between a prime and a non powerful number. ;


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