Problem Statement

Idoneal numbers (also called suitable numbers or convenient numbers) are the positive integers D such that any integer expressible in only one way as x2 ± Dy2 (where x2 is relatively prime to Dy2) is a prime power or twice a prime power. A positive integer n is idoneal if and only if it cannot be written as ab + bc + ac for distinct positive integers a, b, and c with 0 < a < b < c. There are only 65 known iodoneal numbers and is likely that no others exist. If there are others, it has been proven that there are at most, two more, and that no others exist below 1,000,000.

Let's start with the solution:

import "./fmt" for Fmt

var isIdoneal = Fn.new { |n|
    for (a in 1...n) {
        for (b in a+1...n) {
            if (a*b + a + b > n) break
            for (c in b+1...n) {
                var sum = a*b + b*c + a*c
                if (sum == n) return false
                if (sum > n) break
            }
        }
    }
    return true
}

var idoneals = []
for (n in 1..1850) if (isIdoneal.call(n)) idoneals.add(n)
Fmt.tprint("$4d", idoneals, 13)