def test_rand(self):
def divisors_ref(num):
l = [a for a in range(2, num) if num % a == 0]
if len(l) == 0:
return str(num) + " is prime"
return l
a = randint(2, 100)
b = randint(2, 100)
c = randint(2, 100)
self.assertEqual(divisors(a), divisors_ref(a))
self.assertEqual(divisors(b), divisors_ref(b))
self.assertEqual(divisors(c), divisors_ref(c))
def order(n, elt):
if elt in coPrime(n):
for i in sorted(divisors(totient(n))):
if elt ** i % n == 1:
return i
else:
return "Element not in set"
def main():
n = input("Enter n: ")
n = int(n)
sum_divisors = sum_ints(divisors(n))
print(sum_divisors)
def is_practical(p_candidate: int) -> bool:
if p_candidate < 1:
return False
if p_candidate == 1:
return True
divisors = list(divisors(p_candidate))
sums = set(divisors)
arity = 1
def get_sums(arity: int):
return [sum(c) for c in combinations(divisors, arity)]
def is_divisor_sum(ds_candidate):
nonlocal arity
nonlocal sums
if ds_candidate in sums:
return True
while arity <= len(divisors):
arity += 1
more_sums = get_sums(arity)
sums = sums.union(more_sums)
if ds_candidate in sums:
return True
return False
for i in range(1, p_candidate):
if not is_divisor_sum(i):
return False
return True
def is_perfect(n):
perfect = False
if n == sum_ints(divisors(n)):
perfect = True
return perfect
def test_three_to_nine():
assert divisors(3) == [1, 3]
assert divisors(4) == [1, 2, 4]
assert divisors(5) == [1, 5]
assert divisors(6) == [1, 2, 3, 6]
assert divisors(7) == [1, 7]
assert divisors(8) == [1, 2, 4, 8]
assert divisors(9) == [1, 3, 9]
def is_prime(number):
if number % 2 == 0:
log("{0} is not prime".format(number))
else:
divisors_list = divisors(number)
if len(divisors_list) > 2:
log("{0} is not prime, here the divisors:{1}".format(
number, divisors_list))
else:
log("{0} is prime, here the divisors:{1}".format(
number, divisors_list))
def find_prime(n):
if n == 1:
return []
prime = []
multi = 1
factor = list(divisors(n))
factor.remove(1)
for i in factor:
if is_prime(i):
prime.append(i)
multi *= i
return prime + find_prime(n // multi)
def is_perfect(number):
log("Perfect number")
divisors_list = divisors(number)
divisors_list.pop()
if sum(divisors_list) == number:
return {'is': True, 'divisors': divisors_list}
return {
'is': False,
}
def test(self):
self.assertEqual(divisors(15), [3, 5])
self.assertEqual(divisors(253), [11, 23])
self.assertEqual(divisors(24), [2, 3, 4, 6, 8, 12])
self.assertEqual(divisors(13), "13 is prime")
self.assertEqual(divisors(3), "3 is prime")
self.assertEqual(divisors(29), "29 is prime")
def factors(n):
'''
A generator that generates the prime factors of n. For example
>>> list(factors(12))
[2,2,3]
Params:
n (int): The operand
Yields:
(int): All the prime factors of n in ascending order.
Raises:
ValueError: When n is <= 1.
'''
keep_going = True
prime_factors = divisors(n)
while keep_going:
keep_going = False
for val in prime_factors:
if divisors(val) > 2:
keep_going = True
prime_factors.append(divisors(val))
return sorted(factors)
def test_suite(image_name='images/orig.png',slice_widths=None,n_repeats=10,max_factors=None,no_small=False):
image = SlicedImage(fn=image_name)
if slice_widths is None:
width = image.pix.shape[1]
factors = divisors(width)
if no_small:
factors = filter(lambda x:.5*image.pix.shape[1] > x > .02*image.pix.shape[1], factors)
if max_factors is not None and max_factors < len(factors):
factors = sample(factors, max_factors)
slice_widths = factors
tests = []
for n_slices in slice_widths:
for n_test in range(n_repeats):
print n_slices, n_test
tests.append(slice_test(n_slices,image=image))
for s_in,s_out in tests:
print s_in == s_out, s_in, s_out
print 'success rate: %.2f %%' % (float(len(filter(lambda x: x[0] == x[1],tests)))/len(tests)*100)
def main():
fail = False
i = 1
n = 0
while True:
n += i
limit = math.ceil(math.sqrt(n))
d = divisors(n)
if len(d) > 500:
break;
i += 1
return n
def main():
abundant_numbers = []
for i in range(28123):
if i < sum(divisors(i)):
abundant_numbers.append(i)
a_sums = set()
for a in abundant_numbers:
for b in abundant_numbers:
a_sums.add(a + b)
s = 0
for i in range(28123):
if i not in a_sums:
s += i
return s
def main():
numbers = []
amicable_numbers = set()
for i in range(0, 10000):
numbers.append(divisors(i))
for a in range(len(numbers)):
d_a = sum(numbers[a])
for b in range(len(numbers)):
if a == b:
continue
d_b = sum(numbers[b])
if a == d_b and b == d_a:
amicable_numbers.add(a)
amicable_numbers.add(b)
return sum(amicable_numbers)
def test_five():
assert divisors(5) == [1, 5]
def test_four():
assert divisors(4) == [1, 2, 4]
def test_three():
assert divisors(3) == [1, 3]
def is_amicable_pair(x, y):
if x == y:
return False
else:
return sum(divisors(x)) == y and sum(divisors(y)) == x
def test_ten():
assert divisors(10) == [1, 2, 5, 10]
def test_eight():
assert divisors(8) == [1, 2, 4, 8]
def test_one():
assert divisors(1) == [1]
def test_negatives():
assert 3 not in divisors(7)
assert 5 not in divisors(11)
def test_prime_two_hundred_eight_one():
assert divisors(281) == [1, 281]
def test_two_hundred():
assert divisors(200) == [1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200]
def isamicablepair(x):
if sum(divisors(x)) != x and sum(divisors(sum(divisors(x)))) == x:
return True
return False
def tau(n):
return divisors(n).__len__()
def test_six():
assert divisors(6) == [1, 2, 3, 6]
def test_seven():
assert divisors(7) == [1, 7]
from math import sqrt
from divisors import divisors
def is_amicable_pair(x, y):
if x == y:
return False
else:
return sum(divisors(x)) == y and sum(divisors(y)) == x
if __name__ == '__main__':
divisor_sums = {}
for i in range(1, 10000):
divisor_sums[i] = sum(divisors(i))
amicable_numbers = set()
for k, v in divisor_sums.items():
if k != v:
try:
possible_pair = divisor_sums[v]
except KeyError:
pass
else:
if possible_pair == k:
amicable_numbers.add(k)
amicable_numbers.add(v)
print(sum(amicable_numbers))
def test_nine():
assert divisors(9) == [1, 3, 9]
def is_abundant(n):
return sum(divisors(n)) > n
def test_one_hundred():
assert divisors(100) == [1, 2, 4, 5, 10, 20, 25, 50, 100]
def test_divisors_6(self):
self.assertNotEqual(divisors(6), [1, 2, 3, 7])
def test_prime_seventeen():
assert divisors(17) == [1, 17]
def test_3600():
assert list(divisors(3600)) == [
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45,
48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240,
300, 360, 400, 450, 600, 720, 900, 1200, 1800, 3600
]
def test_100():
assert 50 in divisors(100)
assert 25 in divisors(100)
assert 10 in divisors(100)
def return_divisors_list(num):
# make list into dictionary
return jsonify({'divisors': divisors(num)})
def test_product_of_primes():
assert divisors(901) == [1, 17, 53, 901]
def sigma(n):
sum = 0
for i in divisors(n):
sum = sum + i
return sum
def test_two():
assert divisors(2) == [1, 2]
def test_divisors_88(self):
self.assertEqual(divisors(88), [1, 2, 4, 8, 11, 22, 44, 88])
def is_prime(n):
return n != 1 and divisors(n) == {1, n}
def test_divisors_127(self):
self.assertEqual(divisors(127), [1, 127])