def distinctPrimeFactors(n):
div = divisors(n)
div.remove(1)
toRemove = set()
[toRemove.add(d) for d in div if not isPrime(d)]
return div - toRemove
#==============================================================================
# Evaluate the sum of all the amicable numbers under 10000.
#==============================================================================
from Common import divisors
total = 0
for a in range(1, 10000):
b = sum(divisors(a)) - a
if sum(divisors(b)) - b == a and not a == b:
total += a
print(total)
#=============================================================================== # What is the largest prime factor of the number 600851475143 ? #=============================================================================== from Common import isPrime, divisors print(max([i for i in divisors(600851475143) if isPrime(i)]))
#===============================================================================
# What is the value of the first triangle number to have over five hundred divisors?
#===============================================================================
from Common import divisors, trianglenum
i = 1
while True:
if len(divisors(trianglenum(i))) > 500:
break
i += 1
print(trianglenum(i))
#===============================================================================
# Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.
#===============================================================================
from Common import divisors
bound = 28123
abundants = []
[abundants.append(i) for i in range(1, bound) if sum(divisors(i)) - i > i]
sums = set()
high = 0
length = len(abundants)
for i in range(length):
high = 0
j = i;
while high < bound and j < length:
summed = abundants[i] + abundants[j]
sums.add(summed)
high = summed
j += 1
if abundants[i] * 2 >= bound:
break
print(sum(set(range(1, bound)) - sums))
def distinctPrimeFactors(n):
div = divisors(n)
div.remove(1)
toRemove = set()
[toRemove.add(d) for d in div if not isPrime(d)]
return div - toRemove
