Some BE-numbers are both duplicates and irreducibles: here are the smallest ones:

Duplicates and 2-irreducibles: (up to 10⁷)  A387898

4684, 7865, 8538, 10953, 11986, 12449, 18638, 19893, 23506, 40765, 53318, 53444, 65379, 66681, 72292, 82741, 85485, 90135, 95290, 96981, 99913, 108197, 118261, 119482, 132867, 137529, 138026, 150598, 152499, 170702, 176034, 177348, 184673, 192993, 194285, 197885, 225138, 231278, 231775, 233467, 236380, 265685, 273101, 276586, 279130, 291016, 292916, 297505, 305558, 307605, 318946, 320366, 321307, 327906, 330487, 330747, 331681, 332155, 334283, 337586, 339572, 343426, 344196, 348502, 362389, 363171, 364349, 372925, 374384, 387702, 393746, 395260, 399074, 402475, 402577, 414011, 417538, 418396, 418874, 419981, 422370, 446167, 452739, 457962, 473749, 478437, 483496, 504448, 510486, 510786, 511925, 528822, 532750, 543598, 552664, 554066, 556466, 565505, 569253, 570670, 584969, 587534, 589998, 593890, 600839, 613570, 618294, 618992, 621723, 637849, 652612, 670186, 671275, 673452, 673916, 675323, 677463, 677871, 678637, 682523, 690462, 691544, 701494, 705857, 711914, 713699, 715926, 722629, 722893, 724119, 728161, 728738, 728895, 733215, 748280, 753812, 772839, 773773, 787136, 804098, 811579, 815050, 817115, 828597, 833634, 834129, 834518, 848604, 855479, 882995, 884779, 890958, 906578, 919830, 936130, 947519, 952312, 959585, 962198, 977367, 980074, 990179, 994740, 998806, 1004068, 1013278, 1015878, 1037435, 1046322, 1050015, 1053836, 1053880, 1057627, 1058730, 1060635, 1061678, 1062285, 1062763, 1066185, 1069443, 1075025, 1075206, 1078299, 1082885, 1107219, 1138812, 1164498, 1165086, 1167810, 1171999, 1175290, 1175316, 1200870, 1215536, 1216999, 1218169, 1225009, 1227198, 1229102, 1243308, 1245275, 1252242, 1256205, 1264067, 1332642, 1342834, 1350870, 1356496, 1357270, 1381019, 1412067, 1421771, 1442274, 1455353, 1460107, 1483122, 1487353, 1494807, 1505258, 1526316, 1623941, 1634881, 1636022, 1683792, 1687161, 1689001, 1690549, 1696018, 1713146, 1714379, 1716594, 1718311, 1726917, 1739765, 1744773, 1759918, 1767827, 1776061, 1776630, 1779207, 1781603, 1788109, 1791367, 1798055, 1798173, 1817097, 1820486, 1822457, 1830859, 1838014, 1850614, 1852357, 1864134, 1873196, 1873326, 1885516, 1886785, 1889999, 1912514, 1919370, 1919710, 1926108, 1929944, 1946279, 1946768, 1948690, 1951833, 1956517, 1960842, 1961791, 1965167, 1968623, 1972367, 1974450, 1976713, 1977188, 1980055, 1982589, 1988414, 1993201, 2004574, 2005357, 2007550, 2013536, 2021094, 2023840, 2024074, 2024976, 2025893, 2032732, 2033286, 2033583, 2037034, 2038294, 2040482, 2044892, 2047169, 2047399, 2053276, 2056074, 2061938, 2066847, 2070558, 2085245, 2093010, 2098019, 2102890, 2103379, 2103423, 2104387, 2105714, 2122003, 2122832, 2124871, 2127626, 2133256, 2137986, 2139770, 2143170, 2143473, 2153878, 2154698, 2158626, 2167826, 2178097, 2179645, 2179690, 2181143, 2191127, 2195934, 2198845, 2199748, 2200905, 2201797, 2208250, 2211633, 2212597, 2212630, 2216685, 2219050, 2223678, 2224485, 2226113, 2231789, 2232037, 2232098, 2232280, 2233872, 2234233, 2236449, 2237977, 2241097, 2243148, 2245161, 2245378, 2250758, 2251563, 2252812, 2255174, 2258554, 2260058, 2261334, 2261766, 2262467, 2263193, 2266103, 2266726, 2271230, 2273306, 2280860, 2292172, 2295274, 2298034, 2302570, 2303639, 2308182, 2309135, 2312150, 2312620, 2313085, 2316785, 2317006, 2317013, 2319026, 2328918, 2329896, 2333162, 2335082, 2345360, 2348855, 2349180, 2350120, 2350507, 2351395, 2352106, 2357233, 2358375, 2360429, 2360633, 2362435, 2363955, 2365148, 2371718, 2385501, 2392362, 2392390, 2392541, 2400687, 2426440, 2428710, 2440435, 2450501, 2455079, 2456840, 2458743, 2476525, 2476725, 2477602, 2479634, 2481167, 2485967, 2487656, 2487905, 2492636, 2495272, 2496226, 2496291, 2497627, 2499037, 2499175, 2499762, 2500073, 2501520, 2503306, 2503584, 2503676, 2506139, 2509843, 2510475, 2513985, 2517263, 2517903, 2518654, 2518902, 2522724, 2522982, 2525215, 2526571, 2529006, 2534320, 2535319, 2535622, 2538681, 2539071, 2553398, 2554515, 2564938, 2567211, 2567982, 2569937, 2570699, 2580867, 2584682, 2589223, 2603417, 2608908, 2609496, 2611946, 2619662, 2623364, 2624051, 2626109, 2627706, 2631600, 2634640, 2637182, 2639673, 2640696, 2641690, 2641846, 2642212, 2643119, 2651704, 2655067, 2665643, 2666299, 2676999, 2683346, 2691098, 2702571, 2703322, 2707532, 2708194, 2726430, 2732867, 2735768, 2737807, 2738806, 2741322, 2744281, 2744553, 2747545, 2754480, 2754817, 2755472, 2761118, 2762529, 2763241, 2768025, 2774051, 2797584, 2797603, 2821211, 2823271, 2827216, 2834910, 2836125, 2841706, 2842762, 2855354, 2873512, 2882083, 2883318, 2884417, 2885750, 2894089, 2897621, 2902140, 2902378, 2914978, 2918863, 2930351, 2937990, 2943643, 2945931, 2951967, 2961408, 2964548, 2975137, 2979168, 3004385, 3012816, 3017870, 3019920, 3034543, 3043051, 3044582, 3050482, 3053910, 3062721, 3077170, 3078064, 3078864, 3079620, 3086416, 3088913, 3102645, 3109569, 3121862, 3134834, 3137259, 3144536, 3155025, 3155102, 3164219, 3181090, 3196386, 3230195, 3238248, 3245446, 3255749, 3275238, 3283326, 3284050, 3289757, 3317070, 3323720, 3365506, 3373462, 3380324, 3380563, 3385408, 3409021, 3419184, 3419677, 3425342, 3425506, 3432195, 3434201, 3436696, 3453186, 3458712, 3460706, 3464494, 3474074, 3514847, 3518702, 3518806, 3525302, 3532154, 3535299, 3536909, 3538773, 3552705, 3553604, 3556186, 3561848, 3573187, 3573913, 3576215, 3576907, 3666399, 3668348, 3671676, 3676025, 3678639, 3707901, 3728136, 3731942, 3739853, 3741438, 3745730, 3753088, 3757786, 3764162, 3768167, 3775101, 3777626, 3778267, 3779962, 3784112, 3785778, 3786862, 3788819, 3790671, 3794337, 3799550, 3800074, 3806056, 3808720, 3827876, 3830640, 3838356, 3853080, 3884490, 3885836, 3892437, 3904459, 3910442, 3914764, 3919512, 3926323, 3950639, 3971596, 3994530, 4008721, 4009702, 4013939, 4018930, 4037681, 4042274, 4057489, 4058016, 4065456, 4067550, 4068124, 4069425, 4086969, 4107335, 4133055, 4136464, 4137940, 4157123, 4169866, 4172318, 4173219, 4187336, 4190221, 4197887, 4197910, 4200560, 4207177, 4208913, 4209711, 4218141, 4221437, 4230611, 4245883, 4246520, 4250691, 4251779, 4252730, 4261064, 4265513, 4270462, 4284171, 4315871, 4325200, 4326200, 4330964, 4346471, 4350423, 4353963, 4356261, 4365730, 4368830, 4377373, 4387448, 4409497, 4417719, 4432874, 4441530, 4444389, 4447182, 4451191, 4451542, 4454232, 4454932, 4466445, 4468205, 4481201, 4488645, 4502211, 4522032, 4523586, 4525210, 4525847, 4525902, 4539164, 4544934, 4546000, 4550844, 4569313, 4573102, 4580295, 4589427, 4590398, 4591491, 4594890, 4595219, 4595234, 4600546, 4611227, 4614400, 4624611, 4638249, 4643424, 4643903, 4647629, 4648002, 4648707, 4659021, 4669760, 4678889, 4703162, 4713394, 4720782, 4727186, 4778112, 4781029, 4784570, 4784589, 4787967, 4790302, 4797899, 4798960, 4799708, 4806110, 4809422, 4818037, 4819222, 4831134, 4836570, 4836587, 4838814, 4839530, 4840485, 4841842, 4843642, 4848741, 4856243, 4864237, 4868737, 4868950, 4871491, 4872009, 4878298, 4887944, 4894292, 4896116, 4897870, 4898206, 4903483, 4911079, 4921827, 4922379, 4925090, 4927230, 4927437, 4927870, 4935348, 4939899, 4954882, 4958038, 4961092, 4961949, 4967010, 4972556, 4975603, 4980285, 4986957, 4998143, 5003161, 5005009, 5011324, 5012937, 5030721, 5032202, 5038230, 5043543, 5056429, 5058434, 5061579, 5065117, 5068540, 5072312, 5073566, 5077670, 5087929, 5094459, 5095410, 5104583, 5112198, 5115507, 5118678, 5121558, 5127548, 5131223, 5135021, 5138630, 5146358, 5148134, 5154416, 5158247, 5159176, 5167150, 5172927, 5181228, 5182311, 5187361, 5191609, 5203150, 5214476, 5222082, 5224856, 5225484, 5231195, 5231518, 5232615, 5238122, 5239327, 5240839, 5249942, 5258880, 5265313, 5266346, 5276927, 5286195, 5292530, 5297458, 5305877, 5309162, 5309224, 5313374, 5315334, 5316478, 5319071, 5326318, 5330302, 5338651, 5340268, 5340903, 5347475, 5352259, 5374334, 5381289, 5384852, 5394072, 5396050, 5422613, 5431053, 5432180, 5438148, 5438196, 5442578, 5446554, 5454115, 5454426, 5458833, 5475234, 5478365, 5496855, 5508622, 5510235, 5513442, 5513566, 5516349, 5550850, 5563285, 5577279, 5581880, 5602739, 5611199, 5620842, 5630322, 5631685, 5644677, 5645077, 5661856, 5668564, 5669368, 5689386, 5700074, 5712723, 5715810, 5723463, 5733176, 5733717, 5747590, 5767382, 5771234, 5771380, 5777896, 5779065, 5779471, 5783297, 5784441, 5786180, 5787783, 5798395, 5799151, 5811359, 5813994, 5818150, 5821916, 5839001, 5844030, 5847467, 5847561, 5849797, 5851375, 5852736, 5854878, 5857326, 5857535, 5866247, 5875250, 5876060, 5876365, 5885030, 5885882, 5892711, 5895926, 5897734, 5921199, 5925641, 5926050, 5950103, 5952901, 5968619, 5972669, 5974832, 5978253, 5983730, 5985630, 5986002, 5987622, 5991415, 5991950, 5992532, 5995873, 5997392, 5998607, 6000606, 6002998, 6006046, 6006175, 6006367, 6007790, 6010950, 6020124, 6022643, 6024115, 6043373, 6044506, 6047250, 6047612, 6048909, 6048913, 6057707, 6062283, 6063141, 6065985, 6069766, 6069966, 6074186, 6075541, 6076908, 6077474, 6078267, 6079998, 6082515, 6085721, 6087293, 6088211, 6088529, 6097387, 6098022, 6103351, 6105776, 6106458, 6107167, 6107390, 6112793, 6113245, 6113392, 6114587, 6123838, 6124030, 6124049, 6125167, 6125339, 6126322, 6131740, 6133050, 6133326, 6133958, 6137098, 6139200, 6139207, 6141294, 6142763, 6149547, 6151003, 6161907, 6166000, 6166757, 6166815, 6168680, 6170758, 6174653, 6176420, 6180281, 6185516, 6191887, 6202006, 6212851, 6213608, 6219454, 6225140, 6226259, 6227136, 6227661, 6232833, 6233912, 6239182, 6253738, 6259294, 6263955, 6271986, 6278857, 6283122, 6285925, 6295712, 6301285, 6306363, 6306433, 6313440, 6313811, 6315850, 6316350, 6317207, 6320006, 6320723, 6322662, 6324389, 6328014, 6329971, 6334219, 6340782, 6343117, 6343259, 6344766, 6345156, 6345206, 6346054, 6347236, 6347813, 6349546, 6353027, 6358560, 6361121, 6366435, 6368179, 6372222, 6377298, 6381472, 6382790, 6387071, 6388850, 6389162, 6392180, 6397198, 6398475, 6410485, 6410716, 6412562, 6417458, 6423906, 6428638, 6429400, 6429701, 6435506, 6436070, 6445328, 6449219, 6453212, 6455819, 6460443, 6465012, 6469654, 6479505, 6482954, 6488604, 6499294, 6514702, 6515226, 6515274, 6522098, 6523678, 6524822, 6525836, 6535995, 6546478, 6569068, 6571258, 6575141, 6576640, 6578562, 6585227, 6587933, 6592387, 6597592, 6601997, 6602782, 6605233, 6614015, 6614338, 6617394, 6622774, 6623942, 6627591, 6637149, 6638494, 6639450, 6641084, 6641205, 6645140, 6648939, 6649093, 6650759, 6651107, 6657872, 6662329, 6666041, 6672628, 6676957, 6678298, 6680319, 6680402, 6680915, 6687124, 6697576, 6699887, 6701283, 6704646, 6707966, 6708252, 6710446, 6716819, 6723301, 6724577, 6725383, 6725465, 6726013, 6729987, 6741216, 6744859, 6745139, 6746486, 6746766, 6746838, 6748104, 6748713, 6749765, 6754950, 6756004, 6763553, 6768035, 6770226, 6775359, 6782463, 6785010, 6791471, 6797286, 6797408, 6799512, 6801179, 6805340, 6805342, 6810582, 6810712, 6814910, 6815705, 6820068, 6820578, 6821436, 6826427, 6827385, 6827514, 6829259, 6837289, 6837891, 6837906, 6838888, 6841383, 6841846, 6843556, 6845512, 6846986, 6849086, 6852569, 6853026, 6855314, 6856907, 6857471, 6859715, 6860708, 6860746, 6861122, 6861877, 6864573, 6865436, 6870005, 6872076, 6878784, 6879453, 6880113, 6880232, 6882939, 6885827, 6888151, 6889852, 6896408, 6896639, 6898932, 6899320, 6899909, 6900301, 6900808, 6907949, 6908886, 6910262, 6912515, 6914830, 6916408, 6917242, 6919720, 6921292, 6925903, 6928433, 6929235, 6929432, 6931062, 6937490, 6940264, 6946632, 6950126, 6950231, 6952819, 6954851, 6955919, 6956906, 6961022, 6961612, 6969529, 6969952, 6971866, 6976777, 6981376, 6992097, 6995182, 6999002, 7000272, 7001691, 7004154, 7005224, 7006189, 7009192, 7011622, 7020056, 7028467, 7029606, 7029874, 7033111, 7034515, 7045035, 7047267, 7047403, 7048909, 7053803, 7054315, 7055294, 7056990, 7062546, 7067692, 7075841, 7080167, 7082486, 7082926, 7085817, 7089233, 7093294, 7098612, 7100715, 7114310, 7121998, 7122391, 7128635, 7134863, 7135139, 7149534, 7154087, 7165512, 7172568, 7172792, 7178046, 7183095, 7183701, 7183846, 7184793, 7194779, 7195354, 7199077, 7202671, 7206222, 7209725, 7213034, 7218496, 7221204, 7228120, 7228992, 7233064, 7234739, 7240621, 7246841, 7254046, 7258795, 7259402, 7274793, 7279925, 7281247, 7283173, 7284074, 7285777, 7285786, 7288998, 7290315, 7290435, 7290742, 7295000, 7295483, 7295553, 7297063, 7298960, 7302464, 7310399, 7312662, 7315738, 7316069, 7316807, 7318106, 7323395, 7327479, 7338650, 7341202, 7341418, 7347080, 7347881, 7358978, 7367618, 7368363, 7370115, 7374409, 7380645, 7392079, 7392314, 7392878, 7393942, 7408264, 7412827, 7423261, 7424937, 7427356, 7447663, 7471431, 7473533, 7479535, 7488219, 7503852, 7511479, 7533309, 7536402, 7542500, 7543190, 7553787, 7556870, 7561010, 7566302, 7572906, 7575528, 7585405, 7604424, 7613595, 7613794, 7617310, 7618584, 7620663, 7627786, 7640210, 7645619, 7647046, 7648790, 7650953, 7652313, 7656746, 7675979, 7679971, 7682755, 7687620, 7688916, 7697462, 7710162, 7715258, 7723404, 7729914, 7731082, 7732794, 7737539, 7742180, 7748698, 7751252, 7753147, 7754986, 7760483, 7767492, 7769458, 7773963, 7774515, 7775690, 7784226, 7784910, 7786207, 7788491, 7792214, 7794534, 7795259, 7797057, 7802234, 7802818, 7803976, 7806528, 7807561, 7809346, 7812703, 7812934, 7813923, 7814126, 7816735, 7817122, 7822594, 7826467, 7829210, 7835448, 7835722, 7836872, 7840676, 7846954, 7849024, 7851139, 7852623, 7855336, 7868434, 7869238, 7874109, 7884735, 7885263, 7885568, 7893968, 7898231, 7899098, 7901782, 7903304, 7905247, 7908048, 7921263, 7926918, 7927693, 7932203, 7946331, 7948490, 7950573, 7953850, 7971708, 7981307, 7988037, 7988055, 7992138, 7996740, 7998499, 8003474, 8005589, 8012720, 8013683, 8020860, 8024662, 8025526, 8031520, 8031675, 8038122, 8047489, 8050568, 8056846, 8062997, 8064140, 8066233, 8071498, 8073117, 8073371, 8073624, 8081102, 8082142, 8084667, 8088552, 8089234, 8090264, 8104868, 8112117, 8113391, 8125353, 8138421, 8140377, 8141201, 8143346, 8145299, 8152450, 8155173, 8157344, 8162330, 8166325, 8166623, 8170019, 8172489, 8173307, 8176283, 8179819, 8185320, 8196413, 8196982, 8198869, 8200152, 8212475, 8215903, 8216659, 8218087, 8218827, 8221446, 8226122, 8227119, 8227246, 8255980, 8259975, 8261072, 8270614, 8276162, 8280587, 8282576, 8284109, 8285174, 8300331, 8312088, 8333707, 8338312, 8346511, 8369627, 8369923, 8371193, 8386530, 8414716, 8415494, 8420326, 8421246, 8426523, 8427432, 8432208, 8433287, 8433339, 8434322, 8444648, 8446629, 8448710, 8453879, 8454728, 8463289, 8465334, 8476731, 8480148, 8483511, 8485676, 8501248, 8504120, 8512948, 8518278, 8532740, 8534975, 8544754, 8544890, 8548561, 8549717, 8572992, 8583998, 8595649, 8600851, 8602988, 8625225, 8627281, 8632463, 8633998, 8635670, 8655017, 8658054, 8685842, 8687085, 8691497, 8697490, 8703715, 8712847, 8712865, 8720887, 8721418, 8729246, 8729676, 8734506, 8753905, 8758495, 8766591, 8773759, 8782840, 8787328, 8788048, 8793713, 8802554, 8806533, 8819603, 8820320, 8828890, 8829667, 8830951, 8833328, 8849296, 8864566, 8874259, 8886314, 8887057, 8900393, 8913545, 8928881, 8930506, 8935028, 8935547, 8948229, 8950341, 8954001, 8957027, 8959449, 8974502, 8979129, 8989776, 9003362, 9006824, 9022798, 9023168, 9026098, 9038986, 9039951, 9050763, 9050951, 9053450, 9055101, 9070121, 9076739, 9088176, 9090906, 9092329, 9094272, 9156890, 9178093, 9185235, 9192622, 9218395, 9227502, 9233017, 9234025, 9240723, 9255440, 9255682, 9264214, 9274739, 9282485, 9309786, 9315847, 9317578, 9318480, 9339480, 9359968, 9367979, 9369578, 9383306, 9386339, 9394200, 9417099, 9418249, 9420252, 9424449, 9437741, 9443060, 9449854, 9459256, 9462169, 9480367, 9490410, 9499139, 9499585, 9501771, 9505798, 9506902, 9508543, 9526598, 9531893, 9543746, 9551377, 9555114, 9556921, 9563517, 9569465, 9571241, 9579439, 9584622, 9596003, 9605380, 9606043, 9622166, 9634355, 9641867, 9643937, 9659927, 9670809, 9681975, 9682912, 9692135, 9706831, 9729419, 9740771, 9741383, 9747656, 9752826, 9753458, 9755439, 9756698, 9768024, 9769083, 9775730, 9777686, 9779789, 9785115, 9785138, 9795869, 9804320, 9810351, 9818443, 9820327, 9833948, 9843310, 9849323, 9851546, 9860499, 9861899, 9882420, 9891997, 9895199, 9900233, 9902910, 9904422, 9908330, 9916214, 9926097, 9929670, 9930346, 9939401, 9948510, 9964135, 9977333, 9978668, 9981839, 9982103

Duplicates and 3-irreducibles: (up to 10⁸)  A387899

313323 = 2¹¹ + 4⁵ + 5⁶ + 6⁷ + 7² + 11⁴ = 2¹³ + 3⁸ + 4³ + 5² + 6⁵ + 8⁶ + 13⁴ = 2¹⁴ + 3⁴ + 4⁸ + 5⁷ + 6² + 7⁶ + 8⁵ + 14³
550979 = 2¹⁶ + 3¹¹ + 4⁸ + 5⁶ + 6² + 8³ + 11⁵ + 16⁴ = 2⁷ + 3¹² + 4⁵ + 5⁶ + 6³ + 7⁴ + 12² = 2⁹ + 3¹⁰ + 5⁸ + 8² + 9³ + 10⁵
2035918 = 2¹³ + 3⁵ + 4⁸ + 5⁹ + 8² + 9⁴ + 13³ = 2¹³ + 3⁹ + 4¹⁰ + 5⁸ + 6⁵ + 8² + 9⁶ + 10³ + 13⁴ = 2¹⁷ + 3⁹ + 4¹⁰ + 5⁸ + 6³ + 8⁶ + 9² + 10⁵ + 17⁴
4094727 = 2¹¹ + 3⁸ + 4⁶ + 5⁹ + 6³ + 7⁵ + 8⁷ + 9² + 11⁴ = 2¹³ + 3⁸ + 4⁶ + 5⁹ + 6² + 7⁵ + 8⁷ + 9⁴ + 13³ = 2¹⁴ + 3⁶ + 4¹⁰ + 5⁸ + 6² + 7⁴ + 8⁷ + 10³ + 14⁵
4853691 = 2¹⁴ + 3¹³ + 4⁹ + 5⁸ + 6⁴ + 7⁶ + 8⁷ + 9² + 13⁵ + 14³ = 2²⁰ + 3¹¹ + 4⁷ + 6⁸ + 7³ + 8² + 11⁶ + 20⁴ = 2⁵ + 3¹⁴ + 4⁷ + 5⁶ + 6³ + 7² + 14⁴
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88530329 = 2¹⁶ + 3¹⁵ + 4⁸ + 5⁹ + 6¹⁰ + 7³ + 8² + 9⁶ + 10⁷ + 15⁴ + 16⁵ = 2¹⁸ + 3¹⁰ + 4¹² + 5¹¹ + 6⁹ + 7⁸ + 8² + 9⁷ + 10⁵ + 11⁶ + 12³ + 18⁴ = 2²² + 3¹³ + 4¹¹ + 5¹⁰ + 7⁸ + 8⁵ + 10² + 11³ + 13⁷ + 22⁴
88742037 = 2¹⁷ + 4¹³ + 5⁸ + 6⁹ + 7² + 8⁴ + 9⁷ + 13⁶ + 17⁵ = 2²⁶ + 3¹¹ + 4⁹ + 5¹⁰ + 6³ + 7⁸ + 8⁶ + 9⁷ + 10² + 11⁵ + 26⁴ = 2⁵ + 3¹⁵ + 4² + 5¹¹ + 6³ + 7⁸ + 8⁶ + 11⁷ + 15⁴
89456518 = 2¹⁸ + 3⁵ + 4⁹ + 5¹⁰ + 6³ + 7² + 8⁷ + 9⁸ + 10⁴ + 18⁶ = 2⁶ + 3¹² + 4⁹ + 5¹⁰ + 6⁴ + 7⁵ + 8³ + 9⁸ + 10² + 12⁷ = 2⁹ + 3¹² + 4³ + 5¹⁰ + 6⁴ + 7⁵ + 8⁶ + 9⁸ + 10² + 12⁷
91723431 = 2¹³ + 3¹² + 5¹¹ + 6⁸ + 7⁵ + 8³ + 11² + 12⁷ + 13⁶ = 2²⁴ + 3¹³ + 4¹² + 5⁴ + 6⁹ + 7⁸ + 8² + 9⁵ + 12⁷ + 13⁶ + 24³ = 2²⁶ + 3⁶ + 4¹⁰ + 5³ + 6⁸ + 7² + 8⁴ + 10⁷ + 26⁵
92079748 = 2¹³ + 3⁵ + 4¹² + 5⁴ + 6¹⁰ + 7³ + 10⁷ + 12² + 13⁶ = 2²⁰ + 3¹⁴ + 4⁹ + 5¹⁰ + 6⁸ + 7⁴ + 8³ + 9² + 10⁷ + 14⁵ + 20⁶ = 2²³ + 3⁴ + 4⁷ + 6² + 7⁹ + 8⁶ + 9⁸ + 23³
92980535 = 2¹² + 3¹³ + 4³ + 5¹⁰ + 6⁹ + 7⁸ + 8⁵ + 9⁴ + 10² + 12⁶ + 13⁷ = 2⁶ + 3¹² + 4⁹ + 5¹¹ + 6⁷ + 7⁵ + 8³ + 9⁸ + 11⁴ + 12² = 2⁹ + 3¹² + 4³ + 5¹¹ + 6⁷ + 7⁵ + 8⁶ + 9⁸ + 11⁴ + 12²
94440397 = 2¹⁴ + 3⁸ + 4¹³ + 5¹⁰ + 6⁹ + 7⁴ + 8⁷ + 9² + 10³ + 13⁶ + 14⁵ = 2¹⁹ + 3⁴ + 4¹² + 5¹⁰ + 6⁹ + 7² + 9³ + 10⁷ + 12⁵ + 19⁶ = 2²³ + 3¹⁵ + 4⁹ + 5¹¹ + 6⁴ + 7² + 9⁷ + 11³ + 15⁶ + 23⁵
95007700 = 2¹¹ + 3¹⁵ + 4¹² + 5¹⁰ + 6³ + 7⁹ + 9² + 10⁷ + 11⁴ + 12⁶ + 15⁵ = 2¹³ + 3¹⁵ + 4¹² + 5¹⁰ + 6² + 7⁹ + 9⁴ + 10⁷ + 12⁶ + 13³ + 15⁵ = 2¹⁹ + 3¹⁶ + 4⁸ + 5¹¹ + 8² + 11³ + 16⁴ + 19⁵
98785699 = 2¹¹ + 3¹⁶ + 4³ + 5¹⁰ + 6⁸ + 7⁹ + 8⁷ + 9⁵ + 10⁴ + 11⁶ + 16² = 2¹³ + 3¹⁴ + 4⁷ + 5¹⁰ + 6² + 7⁹ + 8⁶ + 9⁸ + 10⁴ + 13³ + 14⁵ = 2¹⁴ + 3¹⁵ + 4⁸ + 5⁹ + 6¹⁰ + 7² + 8³ + 9⁴ + 10⁷ + 14⁵ + 15⁶
99589323 = 2¹¹ + 3¹⁶ + 4¹² + 5¹⁰ + 6⁹ + 7⁶ + 9³ + 10² + 11⁷ + 12⁵ + 16⁴ = 2¹⁶ + 3¹⁰ + 4¹¹ + 5² + 6³ + 7⁹ + 8⁵ + 9⁸ + 10⁷ + 11⁶ + 16⁴ = 2¹⁷ + 3¹³ + 4² + 5¹¹ + 6⁸ + 7⁹ + 8⁷ + 9⁵ + 11⁴ + 13⁶ + 17³

Duplicates and 4-irreducibles:

71286675 = 2²⁰ + 3¹⁰ + 4¹² + 5⁶ + 6⁹ + 8² + 9⁸ + 10⁵ + 12³ + 20⁴ = 2⁶ + 3² + 4⁹ + 6¹⁰ + 7⁸ + 8³ + 9⁷ + 10⁴ = 2⁸ + 3¹⁴ + 4¹¹ + 5³ + 6¹⁰ + 8⁵ + 10² + 11⁶ + 14⁴ = 2⁹ + 3² + 4³ + 6¹⁰ + 7⁸ + 8⁶ + 9⁷ + 10⁴