Найти все натуральные числа из промежутка от 1 до 200, у которых количество делителей равно N

public class Main {
    private static final Map<Integer, List<Integer>> FACTORS_LOOKUP_TABLE;
 
    static {
        FACTORS_LOOKUP_TABLE = new HashMap<>();
 
        FACTORS_LOOKUP_TABLE.put(1, Arrays.asList(1));
        FACTORS_LOOKUP_TABLE.put(2, Arrays.asList(1, 2));
        FACTORS_LOOKUP_TABLE.put(3, Arrays.asList(1, 3));
        FACTORS_LOOKUP_TABLE.put(4, Arrays.asList(1, 2, 4));
        FACTORS_LOOKUP_TABLE.put(5, Arrays.asList(1, 5));
        FACTORS_LOOKUP_TABLE.put(6, Arrays.asList(1, 2, 3, 6));
        FACTORS_LOOKUP_TABLE.put(7, Arrays.asList(1, 7));
        FACTORS_LOOKUP_TABLE.put(8, Arrays.asList(1, 2, 4, 8));
        FACTORS_LOOKUP_TABLE.put(9, Arrays.asList(1, 3, 9));
        FACTORS_LOOKUP_TABLE.put(10, Arrays.asList(1, 2, 5, 10));
        FACTORS_LOOKUP_TABLE.put(11, Arrays.asList(1, 11));
        FACTORS_LOOKUP_TABLE.put(12, Arrays.asList(1, 2, 3, 4, 6, 12));
        FACTORS_LOOKUP_TABLE.put(13, Arrays.asList(1, 13));
        FACTORS_LOOKUP_TABLE.put(14, Arrays.asList(1, 2, 7, 14));
        FACTORS_LOOKUP_TABLE.put(15, Arrays.asList(1, 3, 5, 15));
        FACTORS_LOOKUP_TABLE.put(16, Arrays.asList(1, 2, 4, 8, 16));
        FACTORS_LOOKUP_TABLE.put(17, Arrays.asList(1, 17));
        FACTORS_LOOKUP_TABLE.put(18, Arrays.asList(1, 2, 3, 6, 9, 18));
        FACTORS_LOOKUP_TABLE.put(19, Arrays.asList(1, 19));
        FACTORS_LOOKUP_TABLE.put(20, Arrays.asList(1, 2, 4, 5, 10, 20));
        FACTORS_LOOKUP_TABLE.put(21, Arrays.asList(1, 3, 7, 21));
        FACTORS_LOOKUP_TABLE.put(22, Arrays.asList(1, 2, 11, 22));
        FACTORS_LOOKUP_TABLE.put(23, Arrays.asList(1, 23));
        FACTORS_LOOKUP_TABLE.put(24, Arrays.asList(1, 2, 3, 4, 6, 8, 12, 24));
        FACTORS_LOOKUP_TABLE.put(25, Arrays.asList(1, 5, 25));
        FACTORS_LOOKUP_TABLE.put(26, Arrays.asList(1, 2, 13, 26));
        FACTORS_LOOKUP_TABLE.put(27, Arrays.asList(1, 3, 9, 27));
        FACTORS_LOOKUP_TABLE.put(28, Arrays.asList(1, 2, 4, 7, 14, 28));
        FACTORS_LOOKUP_TABLE.put(29, Arrays.asList(1, 29));
        FACTORS_LOOKUP_TABLE.put(30, Arrays.asList(1, 2, 3, 5, 6, 10, 15, 30));
        FACTORS_LOOKUP_TABLE.put(31, Arrays.asList(1, 31));
        FACTORS_LOOKUP_TABLE.put(32, Arrays.asList(1, 2, 4, 8, 16, 32));
        FACTORS_LOOKUP_TABLE.put(33, Arrays.asList(1, 3, 11, 33));
        FACTORS_LOOKUP_TABLE.put(34, Arrays.asList(1, 2, 17, 34));
        FACTORS_LOOKUP_TABLE.put(35, Arrays.asList(1, 5, 7, 35));
        FACTORS_LOOKUP_TABLE.put(36, Arrays.asList(1, 2, 3, 4, 6, 9, 12, 18, 36));
        FACTORS_LOOKUP_TABLE.put(37, Arrays.asList(1, 37));
        FACTORS_LOOKUP_TABLE.put(38, Arrays.asList(1, 2, 19, 38));
        FACTORS_LOOKUP_TABLE.put(39, Arrays.asList(1, 3, 13, 39));
        FACTORS_LOOKUP_TABLE.put(40, Arrays.asList(1, 2, 4, 5, 8, 10, 20, 40));
        FACTORS_LOOKUP_TABLE.put(41, Arrays.asList(1, 41));
        FACTORS_LOOKUP_TABLE.put(42, Arrays.asList(1, 2, 3, 6, 7, 14, 21, 42));
        FACTORS_LOOKUP_TABLE.put(43, Arrays.asList(1, 43));
        FACTORS_LOOKUP_TABLE.put(44, Arrays.asList(1, 2, 4, 11, 22, 44));
        FACTORS_LOOKUP_TABLE.put(45, Arrays.asList(1, 3, 5, 9, 15, 45));
        FACTORS_LOOKUP_TABLE.put(46, Arrays.asList(1, 2, 23, 46));
        FACTORS_LOOKUP_TABLE.put(47, Arrays.asList(1, 47));
        FACTORS_LOOKUP_TABLE.put(48, Arrays.asList(1, 2, 3, 4, 6, 8, 12, 16, 24, 48));
        FACTORS_LOOKUP_TABLE.put(49, Arrays.asList(1, 7, 49));
        FACTORS_LOOKUP_TABLE.put(50, Arrays.asList(1, 2, 5, 10, 25, 50));
        FACTORS_LOOKUP_TABLE.put(51, Arrays.asList(1, 3, 17, 51));
        FACTORS_LOOKUP_TABLE.put(52, Arrays.asList(1, 2, 4, 13, 26, 52));
        FACTORS_LOOKUP_TABLE.put(53, Arrays.asList(1, 53));
        FACTORS_LOOKUP_TABLE.put(54, Arrays.asList(1, 2, 3, 6, 9, 18, 27, 54));
        FACTORS_LOOKUP_TABLE.put(55, Arrays.asList(1, 5, 11, 55));
        FACTORS_LOOKUP_TABLE.put(56, Arrays.asList(1, 2, 4, 7, 8, 14, 28, 56));
        FACTORS_LOOKUP_TABLE.put(57, Arrays.asList(1, 3, 19, 57));
        FACTORS_LOOKUP_TABLE.put(58, Arrays.asList(1, 2, 29, 58));
        FACTORS_LOOKUP_TABLE.put(59, Arrays.asList(1, 59));
        FACTORS_LOOKUP_TABLE.put(60, Arrays.asList(1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60));
        FACTORS_LOOKUP_TABLE.put(61, Arrays.asList(1, 61));
        FACTORS_LOOKUP_TABLE.put(62, Arrays.asList(1, 2, 31, 62));
        FACTORS_LOOKUP_TABLE.put(63, Arrays.asList(1, 3, 7, 9, 21, 63));
        FACTORS_LOOKUP_TABLE.put(64, Arrays.asList(1, 2, 4, 8, 16, 32, 64));
        FACTORS_LOOKUP_TABLE.put(65, Arrays.asList(1, 5, 13, 65));
        FACTORS_LOOKUP_TABLE.put(66, Arrays.asList(1, 2, 3, 6, 11, 22, 33, 66));
        FACTORS_LOOKUP_TABLE.put(67, Arrays.asList(1, 67));
        FACTORS_LOOKUP_TABLE.put(68, Arrays.asList(1, 2, 4, 17, 34, 68));
        FACTORS_LOOKUP_TABLE.put(69, Arrays.asList(1, 3, 23, 69));
        FACTORS_LOOKUP_TABLE.put(70, Arrays.asList(1, 2, 5, 7, 10, 14, 35, 70));
        FACTORS_LOOKUP_TABLE.put(71, Arrays.asList(1, 71));
        FACTORS_LOOKUP_TABLE.put(72, Arrays.asList(1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72));
        FACTORS_LOOKUP_TABLE.put(73, Arrays.asList(1, 73));
        FACTORS_LOOKUP_TABLE.put(74, Arrays.asList(1, 2, 37, 74));
        FACTORS_LOOKUP_TABLE.put(75, Arrays.asList(1, 3, 5, 15, 25, 75));
        FACTORS_LOOKUP_TABLE.put(76, Arrays.asList(1, 2, 4, 19, 38, 76));
        FACTORS_LOOKUP_TABLE.put(77, Arrays.asList(1, 7, 11, 77));
        FACTORS_LOOKUP_TABLE.put(78, Arrays.asList(1, 2, 3, 6, 13, 26, 39, 78));
        FACTORS_LOOKUP_TABLE.put(79, Arrays.asList(1, 79));
        FACTORS_LOOKUP_TABLE.put(80, Arrays.asList(1, 2, 4, 5, 8, 10, 16, 20, 40, 80));
        FACTORS_LOOKUP_TABLE.put(81, Arrays.asList(1, 3, 9, 27, 81));
        FACTORS_LOOKUP_TABLE.put(82, Arrays.asList(1, 2, 41, 82));
        FACTORS_LOOKUP_TABLE.put(83, Arrays.asList(1, 83));
        FACTORS_LOOKUP_TABLE.put(84, Arrays.asList(1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84));
        FACTORS_LOOKUP_TABLE.put(85, Arrays.asList(1, 5, 17, 85));
        FACTORS_LOOKUP_TABLE.put(86, Arrays.asList(1, 2, 43, 86));
        FACTORS_LOOKUP_TABLE.put(87, Arrays.asList(1, 3, 29, 87));
        FACTORS_LOOKUP_TABLE.put(88, Arrays.asList(1, 2, 4, 8, 11, 22, 44, 88));
        FACTORS_LOOKUP_TABLE.put(89, Arrays.asList(1, 89));
        FACTORS_LOOKUP_TABLE.put(90, Arrays.asList(1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90));
        FACTORS_LOOKUP_TABLE.put(91, Arrays.asList(1, 7, 13, 91));
        FACTORS_LOOKUP_TABLE.put(92, Arrays.asList(1, 2, 4, 23, 46, 92));
        FACTORS_LOOKUP_TABLE.put(93, Arrays.asList(1, 3, 31, 93));
        FACTORS_LOOKUP_TABLE.put(94, Arrays.asList(1, 2, 47, 94));
        FACTORS_LOOKUP_TABLE.put(95, Arrays.asList(1, 5, 19, 95));
        FACTORS_LOOKUP_TABLE.put(96, Arrays.asList(1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96));
        FACTORS_LOOKUP_TABLE.put(97, Arrays.asList(1, 97));
        FACTORS_LOOKUP_TABLE.put(98, Arrays.asList(1, 2, 7, 14, 49, 98));
        FACTORS_LOOKUP_TABLE.put(99, Arrays.asList(1, 3, 9, 11, 33, 99));
        FACTORS_LOOKUP_TABLE.put(100, Arrays.asList(1, 2, 4, 5, 10, 20, 25, 50, 100));
        FACTORS_LOOKUP_TABLE.put(101, Arrays.asList(1, 101));
        FACTORS_LOOKUP_TABLE.put(102, Arrays.asList(1, 2, 3, 6, 17, 34, 51, 102));
        FACTORS_LOOKUP_TABLE.put(103, Arrays.asList(1, 103));
        FACTORS_LOOKUP_TABLE.put(104, Arrays.asList(1, 2, 4, 8, 13, 26, 52, 104));
        FACTORS_LOOKUP_TABLE.put(105, Arrays.asList(1, 3, 5, 7, 15, 21, 35, 105));
        FACTORS_LOOKUP_TABLE.put(106, Arrays.asList(1, 2, 53, 106));
        FACTORS_LOOKUP_TABLE.put(107, Arrays.asList(1, 107));
        FACTORS_LOOKUP_TABLE.put(108, Arrays.asList(1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108));
        FACTORS_LOOKUP_TABLE.put(109, Arrays.asList(1, 109));
        FACTORS_LOOKUP_TABLE.put(110, Arrays.asList(1, 2, 5, 10, 11, 22, 55, 110));
        FACTORS_LOOKUP_TABLE.put(111, Arrays.asList(1, 3, 37, 111));
        FACTORS_LOOKUP_TABLE.put(112, Arrays.asList(1, 2, 4, 7, 8, 14, 16, 28, 56, 112));
        FACTORS_LOOKUP_TABLE.put(113, Arrays.asList(1, 113));
        FACTORS_LOOKUP_TABLE.put(114, Arrays.asList(1, 2, 3, 6, 19, 38, 57, 114));
        FACTORS_LOOKUP_TABLE.put(115, Arrays.asList(1, 5, 23, 115));
        FACTORS_LOOKUP_TABLE.put(116, Arrays.asList(1, 2, 4, 29, 58, 116));
        FACTORS_LOOKUP_TABLE.put(117, Arrays.asList(1, 3, 9, 13, 39, 117));
        FACTORS_LOOKUP_TABLE.put(118, Arrays.asList(1, 2, 59, 118));
        FACTORS_LOOKUP_TABLE.put(119, Arrays.asList(1, 7, 17, 119));
        FACTORS_LOOKUP_TABLE.put(120, Arrays.asList(1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120));
        FACTORS_LOOKUP_TABLE.put(121, Arrays.asList(1, 11, 121));
        FACTORS_LOOKUP_TABLE.put(122, Arrays.asList(1, 2, 61, 122));
        FACTORS_LOOKUP_TABLE.put(123, Arrays.asList(1, 3, 41, 123));
        FACTORS_LOOKUP_TABLE.put(124, Arrays.asList(1, 2, 4, 31, 62, 124));
        FACTORS_LOOKUP_TABLE.put(125, Arrays.asList(1, 5, 25, 125));
        FACTORS_LOOKUP_TABLE.put(126, Arrays.asList(1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126));
        FACTORS_LOOKUP_TABLE.put(127, Arrays.asList(1, 127));
        FACTORS_LOOKUP_TABLE.put(128, Arrays.asList(1, 2, 4, 8, 16, 32, 64, 128));
        FACTORS_LOOKUP_TABLE.put(129, Arrays.asList(1, 3, 43, 129));
        FACTORS_LOOKUP_TABLE.put(130, Arrays.asList(1, 2, 5, 10, 13, 26, 65, 130));
        FACTORS_LOOKUP_TABLE.put(131, Arrays.asList(1, 131));
        FACTORS_LOOKUP_TABLE.put(132, Arrays.asList(1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132));
        FACTORS_LOOKUP_TABLE.put(133, Arrays.asList(1, 7, 19, 133));
        FACTORS_LOOKUP_TABLE.put(134, Arrays.asList(1, 2, 67, 134));
        FACTORS_LOOKUP_TABLE.put(135, Arrays.asList(1, 3, 5, 9, 15, 27, 45, 135));
        FACTORS_LOOKUP_TABLE.put(136, Arrays.asList(1, 2, 4, 8, 17, 34, 68, 136));
        FACTORS_LOOKUP_TABLE.put(137, Arrays.asList(1, 137));
        FACTORS_LOOKUP_TABLE.put(138, Arrays.asList(1, 2, 3, 6, 23, 46, 69, 138));
        FACTORS_LOOKUP_TABLE.put(139, Arrays.asList(1, 139));
        FACTORS_LOOKUP_TABLE.put(140, Arrays.asList(1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140));
        FACTORS_LOOKUP_TABLE.put(141, Arrays.asList(1, 3, 47, 141));
        FACTORS_LOOKUP_TABLE.put(142, Arrays.asList(1, 2, 71, 142));
        FACTORS_LOOKUP_TABLE.put(143, Arrays.asList(1, 11, 13, 143));
        FACTORS_LOOKUP_TABLE.put(144, Arrays.asList(1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144));
        FACTORS_LOOKUP_TABLE.put(145, Arrays.asList(1, 5, 29, 145));
        FACTORS_LOOKUP_TABLE.put(146, Arrays.asList(1, 2, 73, 146));
        FACTORS_LOOKUP_TABLE.put(147, Arrays.asList(1, 3, 7, 21, 49, 147));
        FACTORS_LOOKUP_TABLE.put(148, Arrays.asList(1, 2, 4, 37, 74, 148));
        FACTORS_LOOKUP_TABLE.put(149, Arrays.asList(1, 149));
        FACTORS_LOOKUP_TABLE.put(150, Arrays.asList(1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150));
        FACTORS_LOOKUP_TABLE.put(151, Arrays.asList(1, 151));
        FACTORS_LOOKUP_TABLE.put(152, Arrays.asList(1, 2, 4, 8, 19, 38, 76, 152));
        FACTORS_LOOKUP_TABLE.put(153, Arrays.asList(1, 3, 9, 17, 51, 153));
        FACTORS_LOOKUP_TABLE.put(154, Arrays.asList(1, 2, 7, 11, 14, 22, 77, 154));
        FACTORS_LOOKUP_TABLE.put(155, Arrays.asList(1, 5, 31, 155));
        FACTORS_LOOKUP_TABLE.put(156, Arrays.asList(1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156));
        FACTORS_LOOKUP_TABLE.put(157, Arrays.asList(1, 157));
        FACTORS_LOOKUP_TABLE.put(158, Arrays.asList(1, 2, 79, 158));
        FACTORS_LOOKUP_TABLE.put(159, Arrays.asList(1, 3, 53, 159));
        FACTORS_LOOKUP_TABLE.put(160, Arrays.asList(1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160));
        FACTORS_LOOKUP_TABLE.put(161, Arrays.asList(1, 7, 23, 161));
        FACTORS_LOOKUP_TABLE.put(162, Arrays.asList(1, 2, 3, 6, 9, 18, 27, 54, 81, 162));
        FACTORS_LOOKUP_TABLE.put(163, Arrays.asList(1, 163));
        FACTORS_LOOKUP_TABLE.put(164, Arrays.asList(1, 2, 4, 41, 82, 164));
        FACTORS_LOOKUP_TABLE.put(165, Arrays.asList(1, 3, 5, 11, 15, 33, 55, 165));
        FACTORS_LOOKUP_TABLE.put(166, Arrays.asList(1, 2, 83, 166));
        FACTORS_LOOKUP_TABLE.put(167, Arrays.asList(1, 167));
        FACTORS_LOOKUP_TABLE.put(168, Arrays.asList(1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168));
        FACTORS_LOOKUP_TABLE.put(169, Arrays.asList(1, 13, 169));
        FACTORS_LOOKUP_TABLE.put(170, Arrays.asList(1, 2, 5, 10, 17, 34, 85, 170));
        FACTORS_LOOKUP_TABLE.put(171, Arrays.asList(1, 3, 9, 19, 57, 171));
        FACTORS_LOOKUP_TABLE.put(172, Arrays.asList(1, 2, 4, 43, 86, 172));
        FACTORS_LOOKUP_TABLE.put(173, Arrays.asList(1, 173));
        FACTORS_LOOKUP_TABLE.put(174, Arrays.asList(1, 2, 3, 6, 29, 58, 87, 174));
        FACTORS_LOOKUP_TABLE.put(175, Arrays.asList(1, 5, 7, 25, 35, 175));
        FACTORS_LOOKUP_TABLE.put(176, Arrays.asList(1, 2, 4, 8, 11, 16, 22, 44, 88, 176));
        FACTORS_LOOKUP_TABLE.put(177, Arrays.asList(1, 3, 59, 177));
        FACTORS_LOOKUP_TABLE.put(178, Arrays.asList(1, 2, 89, 178));
        FACTORS_LOOKUP_TABLE.put(179, Arrays.asList(1, 179));
        FACTORS_LOOKUP_TABLE.put(180, Arrays.asList(1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180));
        FACTORS_LOOKUP_TABLE.put(181, Arrays.asList(1, 181));
        FACTORS_LOOKUP_TABLE.put(182, Arrays.asList(1, 2, 7, 13, 14, 26, 91, 182));
        FACTORS_LOOKUP_TABLE.put(183, Arrays.asList(1, 3, 61, 183));
        FACTORS_LOOKUP_TABLE.put(184, Arrays.asList(1, 2, 4, 8, 23, 46, 92, 184));
        FACTORS_LOOKUP_TABLE.put(185, Arrays.asList(1, 5, 37, 185));
        FACTORS_LOOKUP_TABLE.put(186, Arrays.asList(1, 2, 3, 6, 31, 62, 93, 186));
        FACTORS_LOOKUP_TABLE.put(187, Arrays.asList(1, 11, 17, 187));
        FACTORS_LOOKUP_TABLE.put(188, Arrays.asList(1, 2, 4, 47, 94, 188));
        FACTORS_LOOKUP_TABLE.put(189, Arrays.asList(1, 3, 7, 9, 21, 27, 63, 189));
        FACTORS_LOOKUP_TABLE.put(190, Arrays.asList(1, 2, 5, 10, 19, 38, 95, 190));
        FACTORS_LOOKUP_TABLE.put(191, Arrays.asList(1, 191));
        FACTORS_LOOKUP_TABLE.put(192, Arrays.asList(1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192));
        FACTORS_LOOKUP_TABLE.put(193, Arrays.asList(1, 193));
        FACTORS_LOOKUP_TABLE.put(194, Arrays.asList(1, 2, 97, 194));
        FACTORS_LOOKUP_TABLE.put(195, Arrays.asList(1, 3, 5, 13, 15, 39, 65, 195));
        FACTORS_LOOKUP_TABLE.put(196, Arrays.asList(1, 2, 4, 7, 14, 28, 49, 98, 196));
        FACTORS_LOOKUP_TABLE.put(197, Arrays.asList(1, 197));
        FACTORS_LOOKUP_TABLE.put(198, Arrays.asList(1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198));
        FACTORS_LOOKUP_TABLE.put(199, Arrays.asList(1, 199));
        FACTORS_LOOKUP_TABLE.put(200, Arrays.asList(1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200));
    }
 
    public static void main(String[] args) {
        try (InputStreamReader inputStreamReader = new InputStreamReader(System.in);
             BufferedReader bufferedReader = new BufferedReader(inputStreamReader);) {
 
            String input;
 
            do {
                System.out.println("Enter number (to exit -- type anything that's not an int):");
                input = bufferedReader.readLine();
 
                Optional<List<Integer>> numbers;
 
                try {
                    numbers = getNumbersWithFactorsCount(Integer.parseInt(input));
                } catch (NumberFormatException e) {
                    break;
                }
 
                if (numbers.isPresent())
                    System.out.println("Numbers are : " + numbers.get());
                else
                    System.out.println("There are no such numbers");
 
            }
            while (true);
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
 
    private static Optional<List<Integer>> getNumbersWithFactorsCount(final int n) {
        List<Integer> result = new ArrayList<>();
 
        for (final Map.Entry<Integer, List<Integer>> item : FACTORS_LOOKUP_TABLE.entrySet()) {
            if (item.getValue().size() == n)
                result.add(item.getKey());
        }
 
        if (result.size() == 0)
            return Optional.empty();
        else
            return Optional.of(result);
    }
}