p1.py

#!/usr/bin/env python
# opzi problem 1
# http://opzi.posterous.com/puzzle-1-youre-invited


divisors = {}
def find_divs(x):
    if x not in divisors:
        sub_divs= []
        max = x/2 + 1
        for y in range(1, max):
            if x not in sub_divs:
                if not x % y:
                    sub_divs.append(y)
                    sub_divs + find_divs(y)
        divisors[x] = sub_divs
    return divisors[x]


def subsets(s, x):
    z = sum(s)
    if z < x:
        return True
    elif z == x:
        return False
    sl = []
    for t in s:
        nt = list(s)
        nt.remove(t)
        sl.append(nt)
    for r in sl:
        if not subsets(r, x):
            return False
    return True
         


def main():
    for x in range(1, 554):
        divs = find_divs(x)
        if sum(divs) > x:
            if subsets(divs, x):
                print x


if __name__ == "__main__":
    main()