from sets import Set
from eulertools import sieve, cachesumdiv
divisors = list(sieve(10000))
primes = Set(sieve(10000))
sumdivisors = lambda n: cachesumdiv(n, divisors)-n
amicable = []
skips = Set()
for n in range(1,10000):
if n in skips or n in primes: continue
sn = sumdivisors(n)
if sn <= 10000 and sn != n and sumdivisors(sn) == n:
amicable.append(n+sn)
skips.add(sn)
print sum(amicable)
from eulertools import sieve, cachesumdiv, fast_conjoin as conjoin
from sets import Set
from itertools import count
primes = list(sieve(29000))
sumdivs = lambda n: cachesumdiv(n, primes)
def abundants():
for i in count(1):
if i > 28123: break
sd = sumdivs(i) - i
if sd > i:
yield i
abundants = list(abundants())
possibilities = [False]*28124
for i in abundants:
for j in abundants:
if i + j > 28123: break
possibilities[i+j] = True
sum = 0
for i in range(len(possibilities)):
if not possibilities[i]: sum += i
print sum