def test_proper_divisors():
proper_divisors_cases = [
(1, [1]), (2, [1]), (3, [1]), (4, [1, 2]), (5, [1]), (6, [1, 2, 3]),
(7, [1]), (8, [1, 2, 4]), (9, [1, 3]), (10, [1, 2, 5]), (11, [1]),
(12, [1, 2, 3, 4, 6])
]
for inp, output in proper_divisors_cases:
assert proper_divisors(inp) == output
def main():
table = {}
result = 0
for i in range(1, 10000):
divs_sum = sum(proper_divisors(i))
if divs_sum in table and table[divs_sum] == i:
print(i, divs_sum)
result += divs_sum + i
table[i] = divs_sum
print(result)
def main():
triangle_number = 0
largest = 0
for i in range(1, int(1e100)):
triangle_number += i
num_divs = len(proper_divisors(triangle_number))
if num_divs > largest:
largest = num_divs
print(f'New largest: {triangle_number} -> {largest}')
if largest > 500:
print(f'Answer: {triangle_number}')
break
def main():
total = 100000000
primes_set = set(tqdm(prime_generator(limit=total), total=total))
s = 0
for i in tqdm(primes_set):
flag = True
for d in proper_divisors(i - 1):
if d + (i - 1) // d not in primes_set:
flag = False
break
if flag:
s += i - 1
print(s)
def main():
abundant_sums = set()
abundant_numbers = []
result = 0
for i in range(1, 28124):
divs_sum = sum(proper_divisors(i))
if divs_sum > i:
abundant_numbers.append(i)
for number in abundant_numbers:
if number + i > 28123:
break
abundant_sums.add(i + number)
print(abundant_numbers)
print(abundant_sums)
for i in range(1, 28124):
if i not in abundant_sums:
result += i
print(result)
def d(n: int):
return sum(lib.proper_divisors(n))