code: def test_udivisor_sigma():
      assert [udivisor_sigma(k) for k in range(1, 12)] == [
          1,
          3,
          4,
          5,
          6,
          12,
          8,
          9,
          10,
          18,
          12,
      ]
      assert [udivisor_sigma(k, 3) for k in range(1, 12)] == [
          1,
          9,
          28,
          65,
          126,
          252,
          344,
          513,
          730,
          1134,
          1332,
      ]
      assert udivisor_sigma(23450) == 42432
      assert udivisor_sigma(23450, 0) == 16
      assert udivisor_sigma(23450, 1) == 42432
      assert udivisor_sigma(23450, 2) == 702685000
      assert udivisor_sigma(23450, 4) == 321426961814978248
  
      m = Symbol("m", integer=True)
      k = Symbol("k", integer=True)
      assert udivisor_sigma(m)
      assert udivisor_sigma(m, k)
      assert udivisor_sigma(m).subs(m, 4**9) == 262145
      assert (
          udivisor_sigma(m, k).subs([(m, 4**9), (k, 2)])
          == 68719476737
      )
      assert summation(udivisor_sigma(m), (m, 2, 15)) == 169
  
imports: from sympy.concrete.summations import summation
  from sympy.core.containers import Dict
  from sympy.core.mul import Mul
  from sympy.core.power import Pow
  from sympy.core.singleton import S
  from sympy.core.symbol import Symbol
  from sympy.functions.combinatorial.factorials import factorial
  from sympy.core.numbers import Integer, Rational
  from sympy.external.gmpy import gcd
  from sympy.ntheory import totient, factorint, primefactors, divisors, nextprime, primerange, pollard_rho, perfect_power, multiplicity, multiplicity_in_factorial, divisor_count, primorial, pollard_pm1, divisor_sigma, factorrat, reduced_totient
  from sympy.ntheory.factor_ import smoothness, smoothness_p, proper_divisors, antidivisors, antidivisor_count, core, udivisors, udivisor_sigma, udivisor_count, proper_divisor_count, primenu, primeomega, mersenne_prime_exponent, is_perfect, is_abundant, is_deficient, is_amicable, dra, drm, _perfect_power
  from sympy.testing.pytest import raises, slow
  from sympy.utilities.iterables import capture
label_desc: Use image node_id 15 for calling a global function with example usage: test_udivisor_sigma() without return types