示例#1
0
def abundant_numbers(limit=None):
    from maths.misc import find_divisors
    if limit is None:
        # Infinite sequence
        import itertools
        for i in itertools.count(1,1):
            divisors = find_divisors(i, True)
            if sum(divisors) > i:
                yield i
    
    else:
        # Finite sequence
        for i in xrange(1, limit, 1):
            divisors = find_divisors(i, True)
            if sum(divisors) > i:
                yield i
示例#2
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def reduce_fraction(num, denom):
    from maths.misc import find_divisors
    # Find divisors of num & denom
    proper_divisors = True
    div_n = find_divisors(num, proper_divisors)
    div_d = find_divisors(denom, proper_divisors)
    
    # Find intersection between divisors of numerator and denominator
    intersection = list(div_n.intersection(div_d))
    
    # Sort descending
    intersection.sort()
    intersection.reverse()
    
    for i in intersection:
        # Check that num and denom are still evenly divisible by i
        # Need to check this as we're not only reducing by prime numbers
        # We don't want to "over-reduce"
        if num % i == 0 and denom % i == 0:
            num = num / i
            denom = denom / i 
    return num, denom
示例#3
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Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
If d(a) = b and d(b) = a, where a d.n.e. b, then a and b are an amicable pair and each of a and b are called amicable numbers.

For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.

Evaluate the sum of all the amicable numbers under 10000.
"""


if __name__ == "__main__":
    from maths.misc import find_divisors
    amicable_numbers = {}
    
    for a in xrange(1, 10001, 1):
        if a not in amicable_numbers:
            proper_divisors_a = list(find_divisors(a, True))
            
            divisor_sum_a = sum(proper_divisors_a)
            
            # Ensure that d(a) != a
            if divisor_sum_a == a:
                continue
            
            proper_divisors_b = list(find_divisors(divisor_sum_a, True))
            
            divisor_sum_b = sum(proper_divisors_b)
            if divisor_sum_b == a:
                amicable_numbers[a] = divisor_sum_a
                amicable_numbers[divisor_sum_a] = a
    
    numbers = [nums[1] for nums in amicable_numbers.items()]