Project Euler Problem 23

問題

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 whose proper divisors are less than the number is called deficient and a
number whose proper divisors exceed the number is called abundant.

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.

ソース

require 'mathn'

class Integer
	def divisor_sum
		array = []
		self.prime_division.each do |a|
			a[1].times do
				array.push(a[0])
			end
		end
		count = [1]
		1.upto(array.size - 1) do |n|
			array.combination(n).to_a.each do |c|
				count.push(c.inject(:*))
			end
		end
		count.uniq.inject(:+)
	end

	def abundant?
		self < self.divisor_sum
	end
end

max = 28123
abundant = {}
(1..max).each{|x| abundant[x] = 0 if x.abundant?}
puts ((1..max).to_a - (1..28123).select{|x|
	abundant.keys.select{|g| g < x}.find{|g|
		!abundant[x - g].nil?
	}
}).inject(:+)

解答

4179871

感想

んま〜そのまま組んだら通ったって感じです。。
何も特殊なことしていないので、計算に３０秒くらいかかりますwww
2つの過剰数の和で表せない数を出すために、配列の引き算をしているのがポイントかな？