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何かを書き留める何か

数学や読んだ本について書く何かです。最近は社会人として生き残りの術を学ぶ日々です。

Project Euler Problem 23

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.
http://projecteuler.net/problem=23

2つの過剰数の和で書き表せない正の整数の総和を求める問題。
真の約数の和がその数よりも大きいものを過剰数という。

過剰数の定義通りに特に工夫せずに実装した。

#Problem_023 Non-abundant sums
import itertools
abundant = [a for a in range(1,28123) if sum([x for x in divisors(a) if x != a]) > a]
ambi_dif = set([sum(list(c)) for c in itertools.combinations(abundant,2) if sum(list(c)) < 28123])
ambi_sme = set([x+x for x in abundant if x+x < 28123])
sum(list(set(range(1,28123)).difference(ambi_dif.union(ambi_sme))))

まず過剰数のリストabundantを作り、過剰数の和で表せる数のリストを作り…という具合。