code: def test_holder_formula():
      # semiprime
      assert _holder_formula({3, 5}) == 1
      assert _holder_formula({5, 11}) == 2
      # n in A003277 is always 1
      for n in A003277:
          assert _holder_formula(set(factorint(n).keys())) == 1
      # otherwise
      assert _holder_formula({2, 3, 5, 7}) == 12
  
file_path: sympy/sympy/combinatorics/tests/test_group_numbers.py
imports: from sympy.combinatorics.group_numbers import is_nilpotent_number, is_abelian_number, is_cyclic_number, _holder_formula, groups_count
  from sympy.ntheory.factor_ import factorint
  from sympy.ntheory.generate import prime
  from sympy.testing.pytest import raises
  from sympy import randprime
label_desc: Use image node_id 4 for calling a global function with example usage: test_holder_formula() without return types