Non-abundant sums : Problem 23 : Project Euler : Python Code

Non-abundant sums : Problem 23 : Project Euler

A perfect number is a number for which the sum of its proper divisors is exactly equal to the number. For example, the sum of the proper divisors of 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number.
A number n is called deficient if the sum of its proper divisors is less than n and it is called abundant if this sum exceeds n.
As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, the smallest number that can be written as the sum of two abundant numbers is 24. By mathematical analysis, it can be shown that all integers greater than 28123 can be written as the sum of two abundant numbers. However, this upper limit cannot be reduced any further by analysis even though it is known that the greatest number that cannot be expressed as the sum of two abundant numbers is less than this limit.
Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.

Python Code:

def nonAbundantSums():
    def sumOfDivisors(numb):
        sumD = 0
        if numb == 1:
            return 0
        for d in range(numb/2):
            d = d+1
            if numb%d ==0:
                sumD = sumD + d
        return sumD   
       
    limit = 28123       
    sumNonAbn = 0
    tot = 0
    AbnList = ()
    n = 12
    """ Find all the abundant Numbers"""
    while n <= limit:
        if n < sumOfDivisors(n):
            AbnList = AbnList + (n,)
            tot = tot + 1
        """print n"""   
        n = n+1
    """ A List to mark all the numbers less than limit which can be written as sum of abundant numbers"""
    UniqueAbnList = [0 for i in range(limit+1)]
        
   
    for i in range(tot):
        """ Since the list of abundant numbers is increasing once the limit crosses 15000, the sum will be always > limit """
        if AbnList[i] > 15000:
            break
        for j in range(i,tot):
            if (AbnList[i]+AbnList[j]) <= limit:
                """ Mark the numbers """
                UniqueAbnList[AbnList[i]+AbnList[j]] = 1
            j = j + 1   
        i = i + 1       
    k = 0               
    for i in UniqueAbnList:
        if UniqueAbnList[k] == 0:
            """ Add the unmarked numbers """
            sumNonAbn = sumNonAbn +k
            print k,"Cannot be written as Sum of two Abundant Numbers"
        k = k + 1   
    print sumNonAbn       
nonAbundantSums()