61 lines
1.8 KiB
Julia
61 lines
1.8 KiB
Julia
#=
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Created on 11 Aug 2021
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@author: David Doblas Jiménez
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@email: daviddoji@pm.me
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Solution for Problem 23 of Project Euler
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https://projecteuler.net/problem=23
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=#
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function Problem23()
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#=
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A perfect number is a number for which the sum of its proper divisors is
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exactly equal to the number. For example, the sum of the proper divisors
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of 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect
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number.
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A number n is called deficient if the sum of its proper divisors is less
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than n and it is called abundant if this sum exceeds n.
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As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, the smallest
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number that can be written as the sum of two abundant numbers is 24. By
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mathematical analysis, it can be shown that all integers greater than 28123
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can be written as the sum of two abundant numbers. However, this upper
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limit cannot be reduced any further by analysis even though it is known
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that the greatest number that cannot be expressed as the sum of two
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abundant numbers is less than this limit.
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Find the sum of all the positive integers which cannot be written as the
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sum of two abundant numbers.
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=#
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LIMIT = 28123
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divisorsum = zeros(Int32,LIMIT)
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for i in range(1, LIMIT, step=1)
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for j in range(2i, LIMIT, step=i)
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divisorsum[j] += i
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end
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end
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abundantnums = [i for (i, x) in enumerate(divisorsum) if x > i]
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expressible = falses(LIMIT)
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for i in abundantnums
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for j in abundantnums
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if i + j < LIMIT+1
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expressible[i + j] = true
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else
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break
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end
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end
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end
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ans = sum(i for (i, x) in enumerate(expressible) if x == false)
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return ans
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end
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println("Time to evaluate Problem 23:")
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@time Problem23()
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println("")
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println("Result for Problem 23: ", Problem23())
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