print 'fractions are'
print '\n'.join( [str(a) + '/' + str(b) for a, b in fractions] )
product = [1, 1]
for a, b in fractions:
product[0] *= a
product[1] *= b
from lib import euler
# now simplify the product
while 1:
a_divisors = euler.divisors(product[0])
b_divisors = euler.divisors(product[1])
brk = False
for d in a_divisors[::-1]:
if d in b_divisors:
#print 'dividing by', d
if d == 1:
brk = True
break
else:
product = [product[0]/d, product[1]/d]
#print product
break
if brk:
break
"""Evaluate the sum of all the amicable numbers under 10000.""" from lib import euler d = lambda x: sum(euler.divisors(x)[:-1]) amicables = [] for a in xrange(1, 10000): b = d(a) if b != a and d(b) == a: amicables += [a, b] # might be some duplication print sum(list(set(amicables)))
def is_abundant(n): # special case if n<=1: return False divisors = euler.divisors(n)[:-1] return sum(divisors) > n