def compute():
limit = 10**4
div_sums = sum_divisors_sieve(limit - 1, True)
return sum([n for n in range(limit) if div_sums[n] < limit and div_sums[n] != n and
n == div_sums[div_sums[n]]])
def compute():
limit = 28123
div_sums = sum_divisors_sieve(limit, True)
abundant_numbers = [n for n in range(1, limit + 1) if div_sums[n] > n]
return sum_integers(limit) - sum(set(i + j for i in abundant_numbers for j in abundant_numbers
if i + j <= limit))
from euler import sum_divisors_sieve
limit = 10 ** 6
visited = [0] * (limit + 1)
divisors = sum_divisors_sieve(limit, True)
def compute():
longest_chain, min_longest_chain = 0, 0
for start in range(1, limit):
if not visited[start]:
visited[start] = True
chain = [start]
next_item = divisors[start]
while next_item not in chain and next_item <= limit:
chain.append(next_item)
visited[next_item] = 1
next_item = divisors[next_item]
if next_item <= limit:
chain_length = len(chain) - chain.index(next_item)
if chain_length > longest_chain:
longest_chain = chain_length
min_longest_chain = min(chain[chain.index(next_item) :])
return min_longest_chain
if __name__ == "__main__":
print(compute())
