code: def test_groups_count():
      A000001 = [
          0,
          1,
          1,
          1,
          2,
          1,
          2,
          1,
          5,
          2,
          2,
          1,
          5,
          1,
          2,
          1,
          14,
          1,
          5,
          1,
          5,
          2,
          2,
          1,
          15,
          2,
          2,
          5,
          4,
          1,
          4,
          1,
          51,
          1,
          2,
          1,
          14,
          1,
          2,
          2,
          14,
          1,
          6,
          1,
          4,
          2,
          2,
          1,
          52,
          2,
          5,
          1,
          5,
          1,
          15,
          2,
          13,
          2,
          2,
          1,
          13,
          1,
          2,
          4,
          267,
          1,
          4,
          1,
          5,
          1,
          4,
          1,
          50,
          1,
          2,
          3,
          4,
          1,
          6,
          1,
          52,
          15,
          2,
          1,
          15,
          1,
          2,
          1,
          12,
          1,
          10,
          1,
          4,
          2,
      ]
      for n in range(1, len(A000001)):
          try:
              assert groups_count(n) == A000001[n]
          except ValueError:
              pass
  
      A000679 = [
          1,
          1,
          2,
          5,
          14,
          51,
          267,
          2328,
          56092,
          10494213,
          49487367289,
      ]
      for e in range(1, len(A000679)):
          assert groups_count(2**e) == A000679[e]
  
      A090091 = [1, 1, 2, 5, 15, 67, 504, 9310, 1396077, 5937876645]
      for e in range(1, len(A090091)):
          assert groups_count(3**e) == A090091[e]
  
      A090130 = [1, 1, 2, 5, 15, 77, 684, 34297]
      for e in range(1, len(A090130)):
          assert groups_count(5**e) == A090130[e]
  
      A090140 = [1, 1, 2, 5, 15, 83, 860, 113147]
      for e in range(1, len(A090140)):
          assert groups_count(7**e) == A090140[e]
  
      A232105 = [
          51,
          67,
          77,
          83,
          87,
          97,
          101,
          107,
          111,
          125,
          131,
          145,
          149,
          155,
          159,
          173,
          183,
          193,
          203,
          207,
          217,
      ]
      for i in range(len(A232105)):
          assert groups_count(prime(i + 1) ** 5) == A232105[i]
  
      A232106 = [
          267,
          504,
          684,
          860,
          1192,
          1476,
          1944,
          2264,
          2876,
          4068,
          4540,
          6012,
          7064,
          7664,
          8852,
          10908,
          13136,
      ]
      for i in range(len(A232106)):
          assert groups_count(prime(i + 1) ** 6) == A232106[i]
  
      A232107 = [
          2328,
          9310,
          34297,
          113147,
          750735,
          1600573,
          5546909,
          9380741,
          23316851,
          71271069,
          98488755,
      ]
      for i in range(len(A232107)):
          assert groups_count(prime(i + 1) ** 7) == A232107[i]
  
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 5 for calling a global function with example usage: test_groups_count() without return types