ProjectEuler-023.py

'''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.'''

# Step 1, generate list of all abundant numbers
# Step 2, generate list of all numbers < that are not the product of any two numbers from abundant list
# Step 3, sum the non-product list


def factors(number):
    factors_set = set()
    bottom = 1
    top = number

    while bottom < top:
        if (number % bottom) == 0:
            top = int(number / bottom)
            factors_set.add(bottom)
            factors_set.add(top)
        bottom += 1

    answer = sum(factors_set) - number
    if answer > number:
        abundant_numbers.append(number)


abundant_numbers = []
non_products = set()

# Step 1, list all abundant #'s
#for num in range(1, 28123):
#    factors(num)
#print(abundant_numbers)

# Step 1 solution:
abundant_numbers = [12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234, 240, 246, 252, 258, 260, 264, 270, 272, 276, 280, 282, 288, 294, 300, 304, 306, 308, 312, 318, 320, 324, 330, 336, 340, 342, 348, 350, 352, 354, 360, 364, 366, 368, 372, 378, 380, 384, 390, 392, 396, 400, 402, 408, 414, 416, 420, 426, 432, 438, 440, 444, 448, 450, 456, 460, 462, 464, 468, 474, 476, 480, 486, 490, 492, 498, 500, 504, 510, 516, 520, 522, 528, 532, 534, 540, 544, 546, 550, 552, 558, 560, 564, 570, 572, 576, 580, 582, 588, 594, 600, 606, 608, 612, 616, 618, 620, 624, 630, 636, 640, 642, 644, 648, 650, 654, 660, 666, 672, 678, 680, 684, 690, 696, 700, 702, 704, 708, 714, 720, 726, 728, 732, 736, 738, 740, 744, 748, 750, 756, 760, 762, 768, 770, 774, 780, 784, 786, 792, 798, 800, 804, 810, 812, 816, 820, 822, 828, 832, 834, 836, 840, 846, 852, 858, 860, 864, 868, 870, 876, 880, 882, 888, 894, 896, 900, 906, 910, 912, 918, 920, 924, 928, 930, 936, 940, 942, 945, 948, 952, 954, 960, 966, 968, 972, 978, 980, 984, 990, 992, 996, 1000, 1002, 1008, 1014, 1020, 1026, 1032, 1036, 1038, 1040, 1044, 1050, 1056, 1060, 1062, 1064, 1068, 1074, 1080, 1086, 1088, 1092, 1098, 1100, 1104, 1110, 1116, 1120, 1122, 1128, 1134, 1140, 1144, 1146, 1148, 1152, 1158, 1160, 1164, 1170, 1176, 1180, 1182, 1184, 1188, 1190, 1194, 1200, 1204, 1206, 1212, 1216, 1218, 1220, 1224, 1230, 1232, 1236, 1240, 1242, 1248, 1254, 1260, 1266, 1272, 1278, 1280, 1284, 1288, 1290, 1296, 1300, 1302, 1308, 1312, 1314, 1316, 1320, 1326, 1330, 1332, 1338, 1340, 1344, 1350, 1352, 1356, 1360, 1362, 1368, 1372, 1374, 1376, 1380, 1386, 1392, 1398, 1400, 1404, 1408, 1410, 1416, 1420, 1422, 1428, 1430, 1434, 1440, 1446, 1452, 1456, 1458, 1460, 1464, 1470, 1472, 1476, 1480, 1482, 1484, 1488, 1494, 1496, 1500, 1504, 1506, 1512, 1518, 1520, 1524, 1530, 1536, 1540, 1542, 1548, 1554, 1560, 1566, 1568, 1572, 1575, 1578, 1580, 1584, 1590, 1596, 1600, 1602, 1608, 1610, 1614, 1620, 1624, 1626, 1632, 1638, 1640, 1644, 1650, 1652, 1656, 1660, 1662, 1664, 1668, 1672, 1674, 1680, 1686, 1692, 1696, 1698, 1700, 1704, 1708, 1710, 1716, 1720, 1722, 1728, 1734, 1736, 1740, 1746, 1750, 1752, 1758, 1760, 1764, 1768, 1770, 1776, 1780, 1782, 1788, 1792, 1794, 1800, 1806, 1812, 1818, 1820, 1824, 1830, 1836, 1840, 1842, 1848, 1854, 1856, 1860, 1866, 1870, 1872, 1876, 1878, 1880, 1884, 1888, 1890, 1896, 1900, 1902, 1904, 1908, 1914, 1920, 1926, 1932, 1936, 1938, 1940, 1944, 1950, 1952, 1956, 1960, 1962, 1968, 1974, 1976, 1980, 1984, 1986, 1988, 1992, 1998, 2000, 2002, 2004, 2010, 2016, 2020, 2022, 2024, 2028, 2030, 2034, 2040, 2044, 2046, 2052, 2058, 2060, 2064, 2070, 2072, 2076, 2080, 2082, 2088, 2090, 2094, 2100, 2106, 2112, 2118, 2120, 2124, 2128, 2130, 2136, 2140, 2142, 2148, 2154, 2156, 2160, 2166, 2170, 2172, 2176, 2178, 2180, 2184, 2190, 2196, 2200, 2202, 2205, 2208, 2210, 2212, 2214, 2220, 2226, 2232, 2238, 2240, 2244, 2250, 2256, 2260, 2262, 2268, 2274, 2280, 2286, 2288, 2292, 2296, 2298, 2300, 2304, 2310, 2316, 2320, 2322, 2324, 2328, 2334, 2340, 2346, 2352, 2358, 2360, 2364, 2368, 2370, 2376, 2380, 2382, 2388, 2392, 2394, 2400, 2406, 2408, 2412, 2418, 2420, 2424, 2430, 2432, 2436, 2440, 2442, 2448, 2450, 2454, 2460, 2464, 2466, 2470, 2472, 2478, 2480, 2484, 2490, 2492, 2496, 2500, 2502, 2508, 2514, 2520, 2526, 2530, 2532, 2538, 2540, 2544, 2548, 2550, 2552, 2556, 2560, 2562, 2568, 2574, 2576, 2580, 2584, 2586, 2590, 2592, 2598, 2600, 2604, 2610, 2616, 2620, 2622, 2624, 2628, 2632, 2634, 2640, 2646, 2652, 2658, 2660, 2664, 2670, 2676, 2680, 2682, 2688, 2694, 2700, 2704, 2706, 2712, 2716, 2718, 2720, 2724, 2728, 2730, 2736, 2740, 2742, 2744, 2748, 2750, 2752, 2754, 2760, 2766, 2772, 2778, 2780, 2784, 2790, 2796, 2800, 2802, 2808, 2814, 2816, 2820, 2826, 2828, 2832, 2835, 2838, 2840, 2844, 2850, 2856, 2860, 2862, 2868, 2870, 2874, 2880, 2884, 2886, 2892, 2898, 2900, 2904, 2910, 2912, 2916, 2920, 2922, 2928, 2934, 2940, 2944, 2946, 2952, 2958, 2960, 2964, 2968, 2970, 2976, 2980, 2982, 2988, 2990, 2992, 2994, 2996, 3000, 3006, 3008, 3010, 3012, 3016, 3018, 3020, 3024, 3030, 3036, 3040, 3042, 3048, 3052, 3054, 3060, 3066, 3072, 3078, 3080, 3084, 3090, 3096, 3100, 3102, 3108, 3114, 3120, 3126, 3128, 3132, 3136, 3138, 3140, 3144, 3150, 3156, 3160, 3162, 3164, 3168, 3174, 3180, 3186, 3190, 3192, 3198, 3200, 3204, 3210, 3216, 3220, 3222, 3224, 3228, 3230, 3234, 3240, 3246, 3248, 3250, 3252, 3256, 3258, 3260, 3264, 3270, 3276, 3280, 3282, 3288, 3290, 3294, 3300, 3304, 3306, 3312, 3318, 3320, 3324, 3328, 3330, 3332, 3336, 3340, 3342, 3344, 3348, 3354, 3360, 3366, 3372, 3378, 3380, 3384, 3388, 3390, 3392, 3396, 3400, 3402, 3408, 3410, 3414, 3416, 3420, 3426, 3430, 3432, 3438, 3440, 3444, 3450, 3456, 3460, 3462, 3465, 3468, 3472, 3474, 3480, 3486, 3492, 3496, 3498, 3500, 3504, 3510, 3516, 3520, 3522, 3528, 3534, 3536, 3540, 3546, 3552, 3556, 3558, 3560, 3564, 3570, 3576, 3580, 3582, 3584, 3588, 3594, 3600, 3606, 3608, 3612, 3618, 3620, 3624, 3630, 3636, 3640, 3642, 3648, 3654, 3660, 3666, 3668, 3672, 3678, 3680, 3684, 3690, 3696, 3700, 3702, 3708, 3710, 3712, 3714, 3720, 3724, 3726, 3732, 3738, 3740, 3744, 3750, 3752, 3756, 3760, 3762, 3768, 3770, 3774, 3776, 3780, 3784, 3786, 3792, 3798, 3800, 3804, 3808, 3810, 3816, 3820, 3822, 3828, 3834, 3836, 3840, 3846, 3848, 3850, 3852, 3858, 3860, 3864, 3870, 3872, 3876, 3880, 3882, 3888, 3892, 3894, 3900, 3904, 3906, 3912, 3918, 3920, 3924, 3930, 3936, 3940, 3942, 3944, 3948, 3952, 3954, 3960, 3966, 3968, 3972, 3976, 3978, 3980, 3984, 3990, 3996, 4000, 4002, 4004, 4008, 4014, 4020, 4026, 4030, 4032, 4038, 4040, 4044, 4048, 4050, 4056, 4060, 4062, 4068, 4070, 4074, 4080, 4086, 4088, 4092, 4095, 4098, 4100, 4104, 4110, 4116, 4120, 4122, 4128, 4130, 4134, 4136, 4140, 4144, 4146, 4152, 4158, 4160, 4164, 4170, 4172, 4176, 4180, 4182, 4188, 4194, 4200, 4206, 4212, 4216, 4218, 4220, 4224, 4228, 4230, 4236, 4240, 4242, 4248, 4254, 4256, 4260, 4264, 4266, 4270, 4272, 4278, 4280, 4284, 4288, 4290, 4296, 4300, 4302, 4308, 4312, 4314, 4320, 4326, 4332, 4338, 4340, 4344, 4350, 4352, 4356, 4360, 4362, 4368, 4374, 4380, 4386, 4392, 4396, 4398, 4400, 4404, 4408, 4410, 4416, 4420, 4422, 4424, 4428, 4434, 4440, 4446, 4452, 4458, 4460, 4464, 4470, 4472, 4476, 4480, 4482, 4488, 4494, 4500, 4506, 4508, 4510, 4512, 4518, 4520, 4524, 4530, 4536, 4540, 4542, 4544, 4548, 4550, 4554, 4560, 4564, 4566, 4572, 4576, 4578, 4580, 4584, 4590, 4592, 4596, 4600, 4602, 4608, 4614, 4620, 4624, 4626, 4632, 4638, 4640, 4644, 4648, 4650, 4656, 4660, 4662, 4664, 4668, 4672, 4674, 4676, 4680, 4686, 4690, 4692, 4698, 4700, 4704, 4710, 4712, 4716, 4720, 4722, 4725, 4728, 4730, 4732, 4734, 4736, 4740, 4746, 4752, 4758, 4760, 4764, 4770, 4776, 4780, 4782, 4784, 4788, 4794, 4800, 4806, 4812, 4816, 4818, 4820, 4824, 4830, 4836, 4840, 4842, 4844, 4848, 4854, 4860, 4864, 4866, 4872, 4878, 4880, 4884, 4888, 4890, 4896, 4900, 4902, 4908, 4914, 4920, 4926, 4928, 4932, 4938, 4940, 4944, 4950, 4956, 4960, 4962, 4968, 4970, 4974, 4980, 4984, 4986, 4992, 4998, 5000, 5004, 5010, 5012, 5016, 5020, 5022, 5028, 5032, 5034, 5040, 5046, 5052, 5056, 5058, 5060, 5064, 5068, 5070, 5076, 5080, 5082, 5088, 5094, 5096, 5100, 5104, 5106, 5110, 5112, 5118, 5120, 5124, 5130, 5136, 5140, 5142, 5148, 5152, 5154, 5160, 5166, 5168, 5170, 5172, 5178, 5180, 5184, 5190, 5192, 5196, 5200, 5202, 5208, 5214, 5220, 5226, 5232, 5236, 5238, 5240, 5244, 5248, 5250, 5256, 5260, 5262, 5264, 5268, 5274, 5280, 5286, 5292, 5298, 5300, 5304, 5310, 5312, 5316, 5320, 5322, 5328, 5334, 5336, 5340, 5346, 5348, 5352, 5355, 5358, 5360, 5364, 5368, 5370, 5376, 5380, 5382, 5388, 5390, 5394, 5400, 5404, 5406, 5408, 5412, 5418, 5420, 5424, 5430, 5432, 5436, 5440, 5442, 5448, 5454, 5456, 5460, 5466, 5472, 5478, 5480, 5484, 5488, 5490, 5496, 5500, 5502, 5504, 5508, 5512, 5514, 5516, 5520, 5526, 5530, 5532, 5538, 5540, 5544, 5550, 5556, 5560, 5562, 5568, 5572, 5574, 5576, 5580, 5586, 5592, 5598, 5600, 5604, 5610, 5616, 5620, 5622, 5624, 5628, 5632, 5634, 5640, 5646, 5652, 5656, 5658, 5660, 5664, 5670, 5676, 5680, 5682, 5684, 5688, 5694, 5696, 5700, 5704, 5706, 5712, 5718, 5720, 5724, 5730, 5736, 5740, 5742, 5748, 5754, 5760, 5766, 5768, 5772, 5775, 5776, 5778, 5780, 5784, 5790, 5796, 5800, 5802, 5808, 5810, 5814, 5820, 5824, 5826, 5830, 5832, 5838, 5840, 5844, 5848, 5850, 5852, 5856, 5860, 5862, 5868, 5874, 5880, 5886, 5888, 5892, 5896, 5898, 5900, 5904, 5908, 5910, 5916, 5920, 5922, 5928, 5934, 5936, 5940, 5946, 5950, 5952, 5958, 5960, 5964, 5970, 5976, 5980, 5982, 5984, 5985, 5988, 5992, 5994, 6000, 6006, 6012, 6016, 6018, 6020, 6024, 6030, 6032, 6036, 6040, 6042, 6048, 6050, 6054, 6060, 6066, 6072, 6076, 6078, 6080, 6084, 6090, 6096, 6100, 6102, 6104, 6108, 6114, 6120, 6126, 6132, 6136, 6138, 6140, 6144, 6150, 6156, 6160, 6162, 6168, 6174, 6180, 6186, 6188, 6192, 6198, 6200, 6204, 6208, 6210, 6216, 6220, 6222, 6228, 6230, 6232, 6234, 6240, 6244, 6246, 6248, 6252, 6256, 6258, 6260, 6264, 6270, 6272, 6276, 6280, 6282, 6288, 6292, 6294, 6300, 6306, 6312, 6318, 6320, 6324, 6328, 6330, 6336, 6340, 6342, 6344, 6348, 6354, 6356, 6360, 6366, 6370, 6372, 6378, 6380, 6384, 6390, 6392, 6396, 6400, 6402, 6408, 6412, 6414, 6420, 6424, 6426, 6432, 6435, 6438, 6440, 6444, 6448, 6450, 6456, 6460, 6462, 6464, 6468, 6474, 6480, 6486, 6492, 6496, 6498, 6500, 6504, 6510, 6512, 6516, 6520, 6522, 6524, 6528, 6534, 6536, 6540, 6546, 6552, 6558, 6560, 6564, 6570, 6576, 6580, 6582, 6588, 6592, 6594, 6600, 6606, 6608, 6612, 6615, 6618, 6620, 6624, 6630, 6636, 6640, 6642, 6648, 6650, 6654, 6656, 6660, 6664, 6666, 6672, 6678, 6680, 6684, 6688, 6690, 6692, 6696, 6700, 6702, 6708, 6714, 6720, 6726, 6732, 6738, 6740, 6744, 6748, 6750, 6756, 6760, 6762, 6768, 6774, 6776, 6780, 6784, 6786, 6790, 6792, 6798, 6800, 6804, 6808, 6810, 6816, 6820, 6822, 6825, 6828, 6832, 6834, 6840, 6846, 6848, 6852, 6858, 6860, 6864, 6870, 6876, 6880, 6882, 6888, 6894, 6900, 6906, 6912, 6916, 6918, 6920, 6924, 6930, 6936, 6940, 6942, 6944, 6948, 6952, 6954, 6960, 6966, 6968, 6972, 6976, 6978, 6980, 6984, 6990, 6992, 6996, 7000, 7002, 7008, 7014, 7020, 7026, 7028, 7032, 7038, 7040, 7044, 7050, 7056, 7060, 7062, 7068, 7070, 7072, 7074, 7080, 7084, 7086, 7092, 7098, 7100, 7104, 7110, 7112, 7116, 7120, 7122, 7128, 7134, 7140, 7144, 7146, 7150, 7152, 7158, 7160, 7164, 7168, 7170, 7176, 7180, 7182, 7188, 7192, 7194, 7196, 7200, 7206, 7208, 7210, 7212, 7216, 7218, 7220, 7224, 7230, 7232, 7236, 7240, 7242, 7245, 7248, 7252, 7254, 7260, 7266, 7272, 7278, 7280, 7284, 7290, 7296, 7300, 7302, 7304, 7308, 7314, 7320, 7326, 7332, 7336, 7338, 7340, 7344, 7350, 7356, 7360, 7362, 7364, 7368, 7374, 7380, 7384, 7386, 7392, 7398, 7400, 7404, 7410, 7416, 7420, 7422, 7424, 7425, 7428, 7434, 7436, 7440, 7446, 7448, 7452, 7458, 7460, 7464, 7470, 7476, 7480, 7482, 7488, 7490, 7494, 7500, 7504, 7506, 7512, 7518, 7520, 7524, 7530, 7532, 7536, 7540, 7542, 7544, 7548, 7552, 7554, 7560, 7566, 7568, 7572, 7578, 7580, 7584, 7588, 7590, 7592, 7596, 7600, 7602, 7608, 7614, 7616, 7620, 7626, 7630, 7632, 7638, 7640, 7644, 7650, 7656, 7660, 7662, 7668, 7672, 7674, 7680, 7686, 7692, 7696, 7698, 7700, 7704, 7710, 7716, 7720, 7722, 7728, 7734, 7740, 7744, 7746, 7752, 7756, 7758, 7760, 7764, 7770, 7776, 7780, 7782, 7784, 7788, 7794, 7800, 7806, 7808, 7812, 7818, 7820, 7824, 7830, 7832, 7836, 7840, 7842, 7848, 7854, 7860, 7866, 7868, 7872, 7875, 7878, 7880, 7884, 7888, 7890, 7896, 7900, 7902, 7904, 7908, 7910, 7912, 7914, 7920, 7924, 7926, 7932, 7936, 7938, 7940, 7944, 7950, 7952, 7956, 7960, 7962, 7968, 7974, 7980, 7986, 7992, 7998, 8000, 8004, 8008, 8010, 8016, 8020, 8022, 8024, 8028, 8034, 8036, 8040, 8046, 8050, 8052, 8056, 8058, 8060, 8064, 8070, 8076, 8080, 8082, 8085, 8088, 8092, 8094, 8096, 8100, 8106, 8112, 8118, 8120, 8124, 8130, 8136, 8140, 8142, 8148, 8154, 8160, 8166, 8172, 8176, 8178, 8180, 8184, 8190, 8196, 8200, 8202, 8204, 8208, 8214, 8216, 8220, 8226, 8228, 8232, 8238, 8240, 8244, 8250, 8256, 8260, 8262, 8268, 8272, 8274, 8280, 8286, 8288, 8292, 8296, 8298, 8300, 8304, 8310, 8316, 8320, 8322, 8328, 8330, 8334, 8340, 8344, 8346, 8352, 8358, 8360, 8364, 8370, 8372, 8376, 8380, 8382, 8388, 8394, 8400, 8406, 8412, 8415, 8418, 8420, 8424, 8428, 8430, 8432, 8436, 8440, 8442, 8448, 8450, 8454, 8456, 8460, 8464, 8466, 8470, 8472, 8478, 8480, 8484, 8490, 8496, 8500, 8502, 8505, 8508, 8512, 8514, 8520, 8526, 8528, 8532, 8536, 8538, 8540, 8544, 8550, 8556, 8560, 8562, 8568, 8574, 8576, 8580, 8586, 8592, 8596, 8598, 8600, 8604, 8610, 8616, 8620, 8622, 8624, 8628, 8632, 8634, 8640, 8646, 8652, 8658, 8660, 8664, 8670, 8676, 8680, 8682, 8688, 8694, 8700, 8704, 8706, 8708, 8712, 8718, 8720, 8724, 8730, 8736, 8740, 8742, 8748, 8750, 8754, 8760, 8764, 8766, 8772, 8778, 8780, 8784, 8790, 8792, 8796, 8800, 8802, 8808, 8814, 8816, 8820, 8826, 8832, 8838, 8840, 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19434, 19440, 19446, 19448, 19452, 19456, 19458, 19460, 19464, 19470, 19476, 19480, 19482, 19488, 19494, 19500, 19504, 19506, 19512, 19516, 19518, 19520, 19524, 19530, 19536, 19540, 19542, 19544, 19548, 19550, 19552, 19554, 19560, 19566, 19572, 19578, 19580, 19584, 19590, 19596, 19600, 19602, 19608, 19614, 19620, 19624, 19626, 19628, 19632, 19635, 19638, 19640, 19644, 19650, 19656, 19660, 19662, 19668, 19670, 19674, 19680, 19684, 19686, 19692, 19698, 19700, 19704, 19710, 19712, 19716, 19720, 19722, 19728, 19734, 19740, 19746, 19752, 19758, 19760, 19764, 19768, 19770, 19776, 19780, 19782, 19788, 19794, 19796, 19800, 19806, 19810, 19812, 19818, 19820, 19824, 19830, 19836, 19840, 19842, 19845, 19848, 19852, 19854, 19856, 19860, 19864, 19866, 19872, 19878, 19880, 19884, 19888, 19890, 19896, 19900, 19902, 19908, 19914, 19920, 19926, 19932, 19936, 19938, 19940, 19944, 19950, 19952, 19956, 19960, 19962, 19964, 19968, 19974, 19976, 19980, 19986, 19992, 19998, 20000, 20004, 20010, 20016, 20020, 20022, 20028, 20034, 20040, 20046, 20048, 20052, 20058, 20060, 20064, 20070, 20072, 20076, 20080, 20082, 20088, 20090, 20094, 20096, 20100, 20104, 20106, 20112, 20118, 20120, 20124, 20128, 20130, 20132, 20136, 20140, 20142, 20148, 20150, 20152, 20154, 20160, 20166, 20172, 20176, 20178, 20180, 20184, 20188, 20190, 20196, 20200, 20202, 20208, 20214, 20216, 20220, 20224, 20226, 20230, 20232, 20238, 20240, 20244, 20250, 20256, 20260, 20262, 20268, 20272, 20274, 20280, 20286, 20292, 20298, 20300, 20304, 20310, 20316, 20320, 20322, 20328, 20332, 20334, 20336, 20340, 20346, 20350, 20352, 20356, 20358, 20360, 20364, 20368, 20370, 20376, 20380, 20382, 20384, 20388, 20394, 20400, 20406, 20412, 20416, 20418, 20420, 20424, 20430, 20436, 20440, 20442, 20448, 20454, 20460, 20466, 20468, 20472, 20475, 20478, 20480, 20482, 20484, 20488, 20490, 20496, 20500, 20502, 20504, 20508, 20510, 20514, 20520, 20524, 20526, 20532, 20538, 20540, 20544, 20550, 20552, 20556, 20560, 20562, 20568, 20570, 20574, 20580, 20586, 20592, 20598, 20600, 20604, 20608, 20610, 20616, 20620, 20622, 20628, 20634, 20636, 20640, 20646, 20650, 20652, 20658, 20660, 20664, 20670, 20672, 20676, 20680, 20682, 20688, 20692, 20694, 20696, 20700, 20706, 20712, 20718, 20720, 20724, 20730, 20736, 20740, 20742, 20748, 20754, 20760, 20766, 20768, 20772, 20776, 20778, 20780, 20784, 20790, 20796, 20800, 20802, 20804, 20808, 20814, 20820, 20826, 20832, 20838, 20840, 20844, 20850, 20856, 20860, 20862, 20864, 20868, 20874, 20880, 20886, 20888, 20892, 20898, 20900, 20904, 20910, 20916, 20920, 20922, 20928, 20930, 20934, 20940, 20944, 20946, 20952, 20958, 20960, 20964, 20970, 20972, 20976, 20980, 20982, 20988, 20992, 20994, 21000, 21006, 21008, 21012, 21018, 21020, 21024, 21028, 21030, 21032, 21036, 21040, 21042, 21048, 21054, 21056, 21060, 21066, 21070, 21072, 21078, 21080, 21084, 21090, 21096, 21100, 21102, 21105, 21108, 21112, 21114, 21120, 21126, 21132, 21138, 21140, 21144, 21150, 21156, 21160, 21162, 21164, 21168, 21174, 21180, 21186, 21192, 21196, 21198, 21200, 21204, 21208, 21210, 21216, 21220, 21222, 21224, 21228, 21234, 21240, 21246, 21248, 21252, 21258, 21260, 21264, 21270, 21276, 21280, 21282, 21288, 21294, 21296, 21300, 21306, 21308, 21312, 21318, 21320, 21324, 21328, 21330, 21336, 21340, 21342, 21344, 21348, 21350, 21354, 21360, 21364, 21366, 21372, 21376, 21378, 21380, 21384, 21390, 21392, 21396, 21400, 21402, 21408, 21414, 21420, 21424, 21426, 21432, 21438, 21440, 21444, 21448, 21450, 21456, 21460, 21462, 21468, 21472, 21474, 21476, 21480, 21486, 21488, 21490, 21492, 21498, 21500, 21504, 21510, 21516, 21520, 21522, 21528, 21532, 21534, 21540, 21546, 21552, 21558, 21560, 21564, 21570, 21576, 21580, 21582, 21584, 21588, 21594, 21600, 21606, 21612, 21616, 21618, 21620, 21624, 21630, 21632, 21636, 21640, 21642, 21644, 21648, 21654, 21660, 21666, 21672, 21678, 21680, 21684, 21690, 21692, 21696, 21700, 21702, 21708, 21712, 21714, 21720, 21726, 21728, 21732, 21735, 21736, 21738, 21740, 21744, 21750, 21756, 21760, 21762, 21768, 21770, 21774, 21780, 21784, 21786, 21792, 21798, 21800, 21804, 21808, 21810, 21812, 21816, 21820, 21822, 21824, 21828, 21834, 21840, 21846, 21850, 21852, 21858, 21860, 21864, 21868, 21870, 21876, 21880, 21882, 21888, 21894, 21896, 21900, 21906, 21910, 21912, 21918, 21920, 21924, 21930, 21936, 21940, 21942, 21944, 21945, 21948, 21952, 21954, 21960, 21966, 21972, 21978, 21980, 21984, 21990, 21996, 22000, 22002, 22008, 22014, 22016, 22020, 22022, 22026, 22032, 22036, 22038, 22040, 22044, 22048, 22050, 22056, 22060, 22062, 22064, 22068, 22074, 22080, 22086, 22088, 22092, 22098, 22100, 22104, 22110, 22116, 22120, 22122, 22128, 22134, 22140, 22144, 22146, 22148, 22152, 22158, 22160, 22164, 22170, 22176, 22180, 22182, 22188, 22190, 22192, 22194, 22200, 22204, 22206, 22212, 22218, 22220, 22224, 22230, 22232, 22236, 22240, 22242, 22248, 22254, 22256, 22260, 22264, 22266, 22272, 22275, 22278, 22280, 22284, 22288, 22290, 22296, 22300, 22302, 22304, 22308, 22314, 22316, 22320, 22326, 22330, 22332, 22338, 22340, 22344, 22350, 22352, 22356, 22360, 22362, 22365, 22368, 22372, 22374, 22380, 22386, 22392, 22398, 22400, 22404, 22410, 22416, 22420, 22422, 22428, 22434, 22440, 22446, 22448, 22452, 22456, 22458, 22460, 22464, 22470, 22476, 22480, 22482, 22484, 22488, 22494, 22496, 22500, 22506, 22512, 22518, 22520, 22524, 22528, 22530, 22536, 22540, 22542, 22548, 22550, 22554, 22560, 22566, 22568, 22572, 22576, 22578, 22580, 22584, 22590, 22596, 22600, 22602, 22608, 22610, 22614, 22616, 22620, 22624, 22626, 22632, 22638, 22640, 22644, 22650, 22652, 22656, 22660, 22662, 22668, 22672, 22674, 22680, 22686, 22692, 22698, 22700, 22704, 22708, 22710, 22716, 22720, 22722, 22724, 22728, 22734, 22736, 22740, 22746, 22750, 22752, 22758, 22760, 22764, 22770, 22776, 22780, 22782, 22784, 22788, 22792, 22794, 22800, 22806, 22812, 22816, 22818, 22820, 22824, 22830, 22836, 22840, 22842, 22848, 22854, 22860, 22866, 22872, 22876, 22878, 22880, 22884, 22890, 22896, 22900, 22902, 22904, 22908, 22912, 22914, 22920, 22926, 22932, 22938, 22940, 22944, 22950, 22956, 22960, 22962, 22968, 22974, 22980, 22984, 22986, 22988, 22990, 22992, 22995, 22998, 23000, 23004, 23010, 23016, 23020, 23022, 23028, 23030, 23034, 23040, 23044, 23046, 23052, 23056, 23058, 23060, 23064, 23070, 23072, 23076, 23080, 23082, 23088, 23094, 23100, 23104, 23106, 23112, 23118, 23120, 23124, 23128, 23130, 23136, 23140, 23142, 23144, 23148, 23154, 23156, 23160, 23166, 23168, 23170, 23172, 23178, 23180, 23184, 23188, 23190, 23192, 23196, 23200, 23202, 23205, 23208, 23212, 23214, 23220, 23226, 23232, 23238, 23240, 23244, 23250, 23256, 23260, 23262, 23268, 23274, 23280, 23286, 23292, 23296, 23298, 23300, 23304, 23310, 23312, 23316, 23320, 23322, 23324, 23328, 23334, 23340, 23346, 23352, 23358, 23360, 23364, 23370, 23376, 23380, 23382, 23388, 23392, 23394, 23400, 23406, 23408, 23412, 23418, 23420, 23424, 23430, 23436, 23440, 23442, 23448, 23450, 23452, 23454, 23460, 23464, 23466, 23472, 23478, 23480, 23484, 23490, 23492, 23496, 23500, 23502, 23504, 23508, 23514, 23520, 23526, 23532, 23538, 23540, 23544, 23548, 23550, 23552, 23556, 23560, 23562, 23568, 23574, 23576, 23580, 23584, 23586, 23590, 23592, 23598, 23600, 23604, 23608, 23610, 23616, 23620, 23622, 23625, 23628, 23632, 23634, 23640, 23646, 23650, 23652, 23658, 23660, 23664, 23670, 23672, 23676, 23680, 23682, 23688, 23694, 23700, 23706, 23712, 23716, 23718, 23720, 23724, 23730, 23736, 23740, 23742, 23744, 23748, 23754, 23760, 23766, 23772, 23778, 23780, 23784, 23790, 23796, 23800, 23802, 23808, 23814, 23816, 23820, 23826, 23828, 23832, 23838, 23840, 23844, 23848, 23850, 23856, 23860, 23862, 23868, 23870, 23874, 23880, 23884, 23886, 23892, 23898, 23900, 23904, 23910, 23912, 23916, 23920, 23922, 23928, 23934, 23936, 23940, 23946, 23952, 23958, 23960, 23964, 23968, 23970, 23976, 23980, 23982, 23988, 23994, 23996, 24000, 24006, 24010, 24012, 24016, 24018, 24020, 24024, 24030, 24036, 24040, 24042, 24048, 24050, 24052, 24054, 24060, 24064, 24066, 24072, 24078, 24080, 24084, 24090, 24096, 24100, 24102, 24108, 24112, 24114, 24120, 24126, 24128, 24132, 24136, 24138, 24140, 24144, 24150, 24156, 24160, 24162, 24164, 24168, 24174, 24180, 24186, 24192, 24198, 24200, 24204, 24208, 24210, 24216, 24220, 24222, 24228, 24232, 24234, 24240, 24244, 24246, 24248, 24252, 24255, 24258, 24260, 24264, 24270, 24272, 24276, 24280, 24282, 24288, 24290, 24294, 24300, 24304, 24306, 24310, 24312, 24318, 24320, 24324, 24330, 24332, 24336, 24340, 24342, 24348, 24354, 24360, 24366, 24372, 24376, 24378, 24380, 24384, 24388, 24390, 24396, 24400, 24402, 24408, 24414, 24416, 24420, 24426, 24430, 24432, 24438, 24440, 24444, 24448, 24450, 24456, 24460, 24462, 24464, 24468, 24472, 24474, 24480, 24486, 24492, 24498, 24500, 24504, 24510, 24516, 24520, 24522, 24528, 24534, 24540, 24544, 24546, 24552, 24556, 24558, 24560, 24564, 24570, 24576, 24580, 24582, 24584, 24588, 24592, 24594, 24596, 24600, 24606, 24612, 24618, 24620, 24624, 24630, 24636, 24640, 24642, 24648, 24650, 24654, 24656, 24660, 24666, 24668, 24672, 24678, 24680, 24684, 24690, 24696, 24700, 24702, 24704, 24708, 24710, 24714, 24720, 24724, 24726, 24728, 24732, 24738, 24740, 24744, 24750, 24752, 24756, 24760, 24762, 24768, 24774, 24780, 24786, 24792, 24798, 24800, 24804, 24808, 24810, 24816, 24820, 24822, 24828, 24832, 24834, 24836, 24840, 24846, 24850, 24852, 24856, 24858, 24860, 24864, 24870, 24876, 24880, 24882, 24885, 24888, 24892, 24894, 24900, 24904, 24906, 24912, 24918, 24920, 24924, 24928, 24930, 24936, 24940, 24942, 24948, 24954, 24960, 24966, 24972, 24976, 24978, 24980, 24984, 24990, 24992, 24996, 25000, 25002, 25004, 25008, 25014, 25020, 25024, 25026, 25032, 25038, 25040, 25044, 25050, 25056, 25060, 25062, 25064, 25068, 25074, 25080, 25086, 25088, 25092, 25098, 25100, 25104, 25110, 25116, 25120, 25122, 25128, 25130, 25134, 25140, 25144, 25146, 25152, 25158, 25160, 25164, 25168, 25170, 25172, 25176, 25180, 25182, 25188, 25194, 25200, 25206, 25212, 25216, 25218, 25220, 25224, 25228, 25230, 25232, 25236, 25240, 25242, 25245, 25248, 25254, 25256, 25260, 25266, 25270, 25272, 25278, 25280, 25284, 25290, 25296, 25300, 25302, 25308, 25312, 25314, 25320, 25326, 25332, 25338, 25340, 25344, 25350, 25356, 25360, 25362, 25368, 25374, 25376, 25380, 25386, 25392, 25396, 25398, 25400, 25404, 25410, 25416, 25420, 25422, 25424, 25428, 25432, 25434, 25440, 25446, 25452, 25456, 25458, 25460, 25464, 25470, 25472, 25476, 25480, 25482, 25488, 25494, 25500, 25506, 25508, 25512, 25515, 25518, 25520, 25524, 25530, 25536, 25540, 25542, 25548, 25550, 25554, 25560, 25564, 25566, 25568, 25572, 25578, 25580, 25584, 25590, 25592, 25596, 25600, 25602, 25608, 25614, 25620, 25626, 25632, 25636, 25638, 25640, 25644, 25648, 25650, 25656, 25660, 25662, 25668, 25674, 25676, 25680, 25686, 25688, 25690, 25692, 25696, 25698, 25700, 25704, 25710, 25716, 25720, 25722, 25728, 25732, 25734, 25740, 25746, 25752, 25758, 25760, 25764, 25770, 25776, 25780, 25782, 25784, 25788, 25792, 25794, 25800, 25806, 25812, 25816, 25818, 25820, 25824, 25830, 25836, 25840, 25842, 25844, 25848, 25850, 25854, 25856, 25860, 25866, 25872, 25878, 25880, 25884, 25890, 25896, 25900, 25902, 25908, 25914, 25916, 25920, 25926, 25928, 25932, 25935, 25938, 25940, 25944, 25950, 25956, 25960, 25962, 25968, 25970, 25974, 25980, 25984, 25986, 25992, 25998, 26000, 26004, 26010, 26012, 26016, 26020, 26022, 26026, 26028, 26034, 26040, 26046, 26048, 26052, 26058, 26060, 26064, 26068, 26070, 26076, 26080, 26082, 26088, 26094, 26096, 26100, 26104, 26106, 26110, 26112, 26118, 26120, 26124, 26128, 26130, 26136, 26140, 26142, 26144, 26145, 26148, 26152, 26154, 26160, 26166, 26172, 26178, 26180, 26184, 26190, 26196, 26200, 26202, 26208, 26214, 26220, 26224, 26226, 26232, 26236, 26238, 26240, 26244, 26250, 26256, 26260, 26262, 26264, 26268, 26274, 26280, 26286, 26288, 26292, 26298, 26300, 26304, 26310, 26312, 26316, 26320, 26322, 26328, 26334, 26340, 26346, 26348, 26350, 26352, 26358, 26360, 26364, 26368, 26370, 26376, 26380, 26382, 26384, 26388, 26390, 26394, 26400, 26404, 26406, 26412, 26416, 26418, 26420, 26424, 26430, 26432, 26436, 26440, 26442, 26448, 26454, 26460, 26466, 26472, 26478, 26480, 26484, 26488, 26490, 26496, 26500, 26502, 26508, 26514, 26516, 26520, 26526, 26530, 26532, 26538, 26540, 26544, 26550, 26556, 26560, 26562, 26565, 26568, 26572, 26574, 26576, 26580, 26586, 26592, 26598, 26600, 26604, 26610, 26616, 26620, 26622, 26624, 26628, 26634, 26640, 26646, 26650, 26652, 26656, 26658, 26660, 26664, 26670, 26676, 26680, 26682, 26684, 26688, 26694, 26700, 26706, 26712, 26718, 26720, 26724, 26728, 26730, 26736, 26740, 26742, 26748, 26752, 26754, 26760, 26766, 26768, 26772, 26775, 26778, 26780, 26784, 26790, 26796, 26800, 26802, 26808, 26810, 26814, 26820, 26824, 26826, 26832, 26838, 26840, 26844, 26850, 26852, 26856, 26860, 26862, 26864, 26868, 26874, 26880, 26884, 26886, 26892, 26898, 26900, 26904, 26908, 26910, 26912, 26916, 26920, 26922, 26928, 26934, 26936, 26940, 26946, 26950, 26952, 26958, 26960, 26964, 26970, 26976, 26980, 26982, 26988, 26992, 26994, 27000, 27006, 27008, 27012, 27016, 27018, 27020, 27024, 27030, 27036, 27040, 27042, 27048, 27054, 27056, 27060, 27066, 27072, 27076, 27078, 27080, 27084, 27090, 27096, 27100, 27102, 27104, 27108, 27114, 27120, 27126, 27132, 27136, 27138, 27140, 27144, 27150, 27156, 27160, 27162, 27168, 27170, 27174, 27180, 27186, 27188, 27192, 27198, 27200, 27204, 27210, 27216, 27220, 27222, 27228, 27230, 27232, 27234, 27240, 27244, 27246, 27248, 27252, 27258, 27260, 27264, 27270, 27272, 27276, 27280, 27282, 27288, 27294, 27300, 27306, 27312, 27318, 27320, 27324, 27328, 27330, 27336, 27340, 27342, 27348, 27352, 27354, 27356, 27360, 27366, 27368, 27370, 27372, 27376, 27378, 27380, 27384, 27390, 27392, 27396, 27400, 27402, 27404, 27405, 27408, 27412, 27414, 27420, 27426, 27432, 27438, 27440, 27444, 27450, 27456, 27460, 27462, 27468, 27472, 27474, 27480, 27486, 27492, 27496, 27498, 27500, 27504, 27510, 27516, 27520, 27522, 27524, 27528, 27534, 27540, 27544, 27546, 27550, 27552, 27558, 27560, 27564, 27570, 27576, 27580, 27582, 27588, 27594, 27600, 27606, 27608, 27612, 27618, 27620, 27624, 27630, 27632, 27636, 27640, 27642, 27648, 27650, 27654, 27660, 27664, 27666, 27672, 27676, 27678, 27680, 27684, 27690, 27692, 27696, 27700, 27702, 27708, 27714, 27720, 27726, 27732, 27738, 27740, 27744, 27748, 27750, 27756, 27760, 27762, 27768, 27774, 27776, 27780, 27786, 27790, 27792, 27798, 27800, 27804, 27808, 27810, 27816, 27820, 27822, 27824, 27828, 27830, 27832, 27834, 27840, 27846, 27852, 27858, 27860, 27864, 27870, 27872, 27876, 27880, 27882, 27888, 27894, 27896, 27900, 27904, 27906, 27912, 27916, 27918, 27920, 27924, 27930, 27936, 27940, 27942, 27944, 27948, 27950, 27954, 27960, 27966, 27968, 27972, 27976, 27978, 27980, 27984, 27990, 27996, 28000, 28002, 28008, 28014, 28016, 28020, 28026, 28028, 28032, 28035, 28038, 28040, 28044, 28050, 28056, 28060, 28062, 28068, 28070, 28072, 28074, 28080, 28084, 28086, 28092, 28098, 28100, 28104, 28110, 28112, 28116, 28120, 28122]

# Step 2
for num in range(1, 28123):
    if num % 1000 == 0:
        print(num)
    for abundant in abundant_numbers:
        if abundant < num:
            remainder = num - abundant
            if remainder in abundant_numbers:
                break
        elif abundant >= num:
            non_products.add(num)
            break

# Step 3
print(len(non_products), sum(non_products), sorted(non_products))