Prime signature

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the prime signature of a number is the <a href="/facts/Multiset/bPFJGMDo">multiset</a> of (nonzero) exponents of its <a href="/facts/Prime_factorization/EjMCTz2t">prime factorization</a>. The prime signature of a number having prime factorization 
  
    
      
        
          p
          
            1
          
          
            
              m
              
                1
              
            
          
        
        
          p
          
            2
          
          
            
              m
              
                2
              
            
          
        
        …
        
          p
          
            n
          
          
            
              m
              
                n
              
            
          
        
      
    
    {\displaystyle p_{1}^{m_{1}}p_{2}^{m_{2}}\dots p_{n}^{m_{n}}}
  
 is the multiset 
  
    
      
        
          {
          
            
              m
              
                1
              
            
            ,
            
              m
              
                2
              
            
            ,
            …
            ,
            
              m
              
                n
              
            
          
          }
        
      
    
    {\displaystyle \left\{m_{1},m_{2},\dots ,m_{n}\right\}}
  
.
</p><p>For example, all <a href="/facts/Prime_number/L20FLkgn">prime numbers</a> have a prime signature of {1}, the <a href="/facts/Square_number/jfakASPK">squares</a> of primes have a prime signature of {2}, the products of 2 distinct primes have a prime signature of {1, 1} and the products of a square of a prime and a different prime (e.g. 12, 18, 20, ...) have a prime signature of {2, 1}.
</p>

Prime signature open-in-new

Prime signature