Jordan's totient function

<p>In <a href="/facts/Number_theory/zhoa7zrc">number theory</a>, Jordan's totient function, denoted as 
  
    
      
        
          J
          
            k
          
        
        (
        n
        )
      
    
    {\displaystyle J_{k}(n)}
  
, where 
  
    
      
        k
      
    
    {\displaystyle k}
  
 is a positive integer, is a function of a <a href="/facts/Positive_integer/u65og8JE">positive integer</a>, 
  
    
      
        n
      
    
    {\displaystyle n}
  
, that equals the number of 
  
    
      
        k
      
    
    {\displaystyle k}
  
-<a href="/facts/Tuple/BI1HIxL8">tuples</a> of positive integers that are less than or equal to 
  
    
      
        n
      
    
    {\displaystyle n}
  
 and that together with 
  
    
      
        n
      
    
    {\displaystyle n}
  
 form a <a href="/facts/Coprime_integers/bnCxCXxs">coprime set</a> of 
  
    
      
        k
        +
        1
      
    
    {\displaystyle k+1}
  
 integers.
</p><p>Jordan's totient function is a generalization of Euler's <a href="/facts/Totient_function/mIQwXYzj">totient function</a>, which is the same as 
  
    
      
        
          J
          
            1
          
        
        (
        n
        )
      
    
    {\displaystyle J_{1}(n)}
  
. The function is named after <a href="/facts/Camille_Jordan/gmLuEJ4e">Camille Jordan</a>.
</p>

Jordan's totient function open-in-new

Jordan's totient function