abundant.
As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, the
smallest number that can be written as the sum of two abundant numbers is
24. By mathematical analysis, it can be shown that all integers greater
than 28123 can be written as the sum of two abundant numbers. However,
this upper limit cannot be reduced any further by analysis even though it
is known that the greatest number that cannot be expressed as the sum of
two abundant numbers is less than this limit.
Find the sum of all the positive integers which cannot be written as the
sum of two abundant numbers.
"""
import euler_utils as utils
divisor_sum = lambda number:sum(utils.divisors_of(number))
abundant_numbers = []
for i in range(12, 28124):
if divisor_sum(i) > i:
abundant_numbers.append(i)
abundant_set = set(abundant_numbers)
total = sum([x for x in range(24)]) #+ sum([x for x in range(25, 28124,2)])
for num in range(25, 28124, 1):
index = 0
isSum = False
For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22,
44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1,
2, 4, 71 and 142; so d(284) = 220.
Evaluate the sum of all the amicable numbers under 10000.
"""
import euler_utils as utils
no_op_set = set(utils.primes_till(10000))
dn_map = {}
amicable_pairs = []
dn = lambda x:sum(utils.divisors_of(x))
for num in range(4,10001):
if num not in no_op_set and num not in dn_map:
dsum = dn(num)
dn_map[num] = dsum
if dsum < 10000 and dsum > num:
dsum_sum = dn(dsum)
if dsum_sum == num:
amicable_pairs.append((num, dsum))
dn_map[dsum] = dsum_sum
print sum([x+y for x,y in amicable_pairs])
