code: def test_tau_hypothesis(n):
      div = divisors(n)
      tau_n = len(div)
      assert is_square(n) == (tau_n % 2 == 1)
      sigmas = [divisor_sigma(i) for i in div]
      totients = [totient(n // i) for i in div]
      mul = [a * b for a, b in zip(sigmas, totients)]
      assert n * tau_n == sum(mul)
  
file_path: sympy/sympy/ntheory/tests/test_hypothesis.py
imports: from hypothesis import given
  from hypothesis import strategies
  from sympy import divisors
  from sympy.ntheory.primetest import is_square
  from sympy.ntheory import totient
  from sympy.ntheory import divisor_sigma
label_desc: Use image node_id 1 for calling a global function with example usage: test_tau_hypothesis(n) without return types