def amicable_pair(a):
b = sum(proper_divisors(a))
c = sum(proper_divisors(b))
if a == c and a != b:
print "amicable pair found: {}, {}".format(a, b)
return a, b
else:
return None, None
def single_pythagorean(L):
factors = sorted(utils.proper_divisors(L / 2))
triplets = []
for m in factors:
if m > math.sqrt(L / 4):
n = L // (2 * m) - m
print(m, n)
if n > 0:
triplet = pythagorean_triplet(m, n)
triplets.append(triplet)
print(triplets)
if len(set(triplets)) > 1:
return False
if len(set(triplets)) == 0:
return False
else:
return True
import utils
d = {}
utils.initialize_primes_cache(10001)
for i in range(1, 10000):
d[i] = sum(utils.proper_divisors(i))
def amicable_pairs():
for i in range(1, 10000):
for j in range(i + 1, 10000):
if d[i] == j and d[j] == i: yield i + j
print(sum(amicable_pairs()))
def sum_of_proper_divisors(n):
divs = proper_divisors(n)
if divs:
return sum(divs)
else:
return 1
def d(n):
"""sum of proper divisors of n."""
return sum(proper_divisors(n))
def abundant(number: int) -> bool:
return sum(proper_divisors(number)) > number
def divisor_sum(n):
return sum(proper_divisors(n))
def amicable(number: int) -> bool:
candidate = sum(proper_divisors(number))
return (sum(proper_divisors(candidate)) == number and candidate != number)
def deficient_number(n):
return sum(proper_divisors(n)) < n
def perfect_number(n):
return sum(proper_divisors(n)) == n
def abundant_number(n):
return sum(proper_divisors(n)) > n
def abundant(n):
return sum(utils.proper_divisors(n)) > n
def is_abundant(n):
condition = sum(utils.proper_divisors(n)) > n
return True if condition else False
def divisor_sum(n):
return sum(proper_divisors(n))