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
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
