def is_abundant(n):
if n == 0:
return False
factors = all_factors(n)
sum = 0
for factor in factors:
sum += factor
sum -= n
return sum > n
def smallest_k(n,min=0): if gcd(n,10) != 1: return None if gcd(n-9,n) != 1: return None # return handle_zero_divisors(n) factors = primes.all_factors(primes.factor(primes.euler_phi(n))) if factors[-1] < min: return None for factor in factors: factor = int(factor) if pow(10,factor,n) == 1: if factor < min: return None return factor
def handle_zero_divisors(n): print "Zero divisors", factors = primes.all_factors(primes.factor(primes.euler_phi(n))) possibilities = PriorityQueue() for factor in factors: factor = int(factor) if pow(10,factor,n) == 1: possibilities.put((factor,factor,1)) if possibilities.empty(): return None while True: #should eventually terminate _,factor,multiple = possibilities.get() if pow(100,factor,n) == 1: print n,factor*multiple return factor*multiple possibilities.put((factor*(multiple*1),factor,multiple+1))
assert (is_prime(29))
assert (is_prime(31))
assert (is_prime(37))
assert (not is_prime(-1))
assert (not is_prime(0))
assert (not is_prime(4))
assert (not is_prime(6))
assert (not is_prime(9))
assert (not is_prime(15))
assert (not is_prime(25))
with timeit("prime_factors test suite"):
assert (list(prime_factors(2)) == [2])
assert (list(prime_factors(3)) == [3])
assert (list(prime_factors(5)) == [5])
assert (list(prime_factors(2 * 3 * 5 * 7 * 11 *
13)) == [2, 3, 5, 7, 11, 13])
assert (list(prime_factors(2 * 2 * 3 * 3 * 5 * 5 * 7 *
7)) == [2, 2, 3, 3, 5, 5, 7, 7])
with timeit("all_factors test suite"):
assert (all_factors(512) == {1, 2, 4, 8, 16, 32, 64, 128, 256, 512})
assert (all_factors(2 * 3 *
5) == {1, 2, 3, 5, 2 * 3, 2 * 5, 3 * 5, 2 * 3 * 5})
with timeit("is_prime perf test"):
assert (is_prime(2**61 - 1))
with timeit("prime_factors perf test"):
assert (list(prime_factors(2**61 - 1)) == [2**61 - 1])
def findPair(n):
sum=0
for x in primes.all_factors(n):sum +=x
sum -= n
return sum
def factorSum(n):
sum=0
for x in primes.all_factors(n):sum +=x
sum -= n
return sum
import primes
MAX = 28124
primes._refresh(MAX/2)
abundants = [n for n in xrange(1, MAX) if sum(primes.all_factors(n)) > n+n]
abundants_dict = dict.fromkeys(abundants, 1)
total = 0
for n in xrange(1, MAX):
sum_of_abundants = 0
for a in abundants:
if a > n: break
if abundants_dict.get(n - a):
sum_of_abundants = 1
break
if not sum_of_abundants:
total = total + n
print total
def get_amicabilibuddy(n):
factors = primes.all_factors(n)
sum = 0
for factor in factors[:-1]:
sum += factor
return sum
