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Calculate the crystallographic restriction in higher dimensions

Posted 5 months ago
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Base on the description in the paper The crystallographic restriction in higher dimensions as shown below:

enter image description here

I try to calculate the crystallographic restriction in higher dimensions using the Euler totient function, however, I found that only the first few results are consistent with the results in this paper, as shown below:

In[749]:= 
ord[n_Integer] := 
 Position[EulerPhi[#] == n & /@ Range[100], True] // Flatten

In[757]:= ord[#] & /@ Range[20]

Out[757]= {{1, 2}, {3, 4, 6}, {}, {5, 8, 10, 12}, {}, {7, 9, 14, 
  18}, {}, {15, 16, 20, 24, 30}, {}, {11, 22}, {}, {13, 21, 26, 28, 
  36, 42}, {}, {}, {}, {17, 32, 34, 40, 48, 60}, {}, {19, 27, 38, 
  54}, {}, {25, 33, 44, 50, 66}}

I am confused where the problem is. Any hints for fixing this result?

Regards,
Zhao

POSTED BY: Hongyi Zhao
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