"""What is the value of the first triangle number to have over five hundred divisors?

The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
    1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

Let us list the factors of the first seven triangle numbers:
     1: 1
     3: 1,3
     6: 1,2,3,6
    10: 1,2,5,10
    15: 1,3,5,15
    21: 1,3,7,21
    28: 1,2,4,7,14,28

We can see that 28 is the first triangle number to have over five divisors.

What is the value of the first triangle number to have over five hundred divisors?
"""

from e003 import pfactor
from p054.poker import unique_combinations

def triangle(n):
    x = 0
    for i in range(n + 1):
        x = x + i
    return x

def badfactor(n):
    f = []
    for i in range(n, 0, -1):
        if n % i == 0:
            f.append(i)
    return f

def product(l):
    p = 1
    for n in l:
        p = p * n
    return p

def factor(n):
    primes = pfactor(n)
    factors = [1, n]
    pow = {}
    for p in primes:
        if p not in pow.keys():
            pow[p] = 0
        pow[p] = pow[p] + 1
        factors.append(p**pow[p])
    
    for p in [f for f in factors if f > 1]:
        f = n / p
        if f not in factors:
            factors.append(n / p)
    combos = unique_combinations(factors, 2)
    for c in combos:
        f = product(c)
        if f < n and n % f == 0 and f not in factors:
            factors.append(f)
    
    if n not in factors:
        factors.append(n)
    
    return sorted(set(factors))
def main():
    i = 1
    while True:
        i = i + 1
        t = triangle(i)
        f = factor(t)
        print 'Checking triangle', i, t, len(f)
        if len(f) > 500:
            break
    
    print 'Triangle number {0} has {1} factors ({2})'.format(t, len(f), f)
if __name__ == '__main__':
    main()