filters - Remove a frequency and all its multiple (harmonics)

In a soundfile, I'd like to remove a frequency and all its harmonics. What is the best solution in your opinion ?

1. 
   

   Do a loop with 20 notch filters, one after another.

   
   

   
   // f is the fundamental frequency
   
   for (i=0; i++; i<21)
   {
   file.notchfilter(f*i);
   }
   

   
   Question : does each notch filter create some unwanted side-effects, and the fact that we use 20 filters one after another will create very high unwanted artefacts?


2. 
   

   Is it possible to design a filter that will remove 20 frequencies in ONE STEP ? Then we wouldn't need to do a loop, just one pass wil be okay? Is it called a Comb filter ?

   
   


3. 
   
   

   Other method ?