/**
 * Non-abundant sums
 *
 * 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.
 *
 * https://projecteuler.net/problem=23
 */
fun main() {
    println(nonAbundantSums())
}

private fun nonAbundantSums(): Int {
    val limit = 28123
    val totalSum = (1..limit).sum()
    val abundants = buildList {
        for (n in 12..limit) {
            if (n.sumOfProperDivisors() > n) {
                add(n)
            }
        }
    }

    val abundantsSums = buildSet {
        for (i in abundants.indices) {
            for (j in i..abundants.lastIndex) {
                val sum = abundants[i] + abundants[j]
                if (sum <= limit) {
                    add(abundants[i] + abundants[j])
                }
            }
        }
    }

    return totalSum - abundantsSums.sum()
}
