def get_sum_of_divisors(primes, n):
prime_factors = []
euler_base.get_prime_factors(primes, prime_factors, n)
divisors = euler_base.get_divisors(prime_factors, n, include_n=False)
divisors.sort()
# print "n: %d, divisors: %s" % (n, divisors)
return sum(divisors)
def main():
"""
600851475143 = 71* 839* 1471* 6857
"""
if len(sys.argv) < 2:
usage()
sys.exit(0)
start = time.time()
n = int(sys.argv[1])
primes = euler_base.get_primes_to_sqrt_n(n)
prime_factors = []
euler_base.get_prime_factors(primes, prime_factors, n)
print "%d has prime factors: %s" % (n, prime_factors)
return previous_tn + n
def main():
"""
What is the value of the first triangle number to have over five hundred divisors?
The 12375th triangle number: 76576500, has 575 divisors
found solution in 35.4850001335 seconds
"""
if len(sys.argv) < 2:
usage()
sys.exit(0)
start = time.time()
n = int(sys.argv[1])
i = 1
tn = 1 # initial triangle number value
primes_step = 100
primes = []
euler_base.get_nth_prime(primes, primes_step) # populate array of primes to start with
while True:
tn = get_nth_triangle_number(tn, i)
min_prime_number = int(math.sqrt(tn))
while primes[-1] < min_prime_number:
# get more primes as needed
euler_base.get_nth_prime(primes, len(primes) + primes_step)
# determine the factors of tn that are prime numbers
prime_factors = []
euler_base.get_prime_factors(primes, prime_factors, tn)
# print "tn: %d, prime_factors: %s" % (tn, prime_factors)
# use list of primes to determine all divisors of tn
divisors = euler_base.get_divisors(set(prime_factors), tn, include_n=True)
# print "divisors: %s" % divisors
if len(divisors) > n: