id
stringlengths
7
11
seq
listlengths
1
347
keywords
listlengths
1
8
A227426_aug
[ 1, 1, 1, 2, 2, 3, 3, 5, 6, 7, 9, 11, 13, 16, 20, 23, 28, 33, 39, 46, 55, 63, 75, 87, 101, 117, 136, 156, 180, 207, 238, 272, 311, 355, 404, 460, 522, 592, 670, 758, 855, 965, 1087, 1223, 1373, 1543, 1728, 1936, 2166, 2...
null
A038088_aug
[ 1, 3, 5, 8, 12, 17, 23, 32, 41, 52, 66, 83, 102, 124, 152, 181, 216, 255, 299, 346, 400, 458, 521, 588, 659, 735, 814, 896, 979, 1067, 1151, 1239, 1324, 1407, 1486, 1564, 1635, 1700, 1759, 1809, 1853, 1887, 1912, 1925, 1932, 1...
null
A329254_aug
[ -1, -3, -4, -5, -6, -7, -8, -9, -191, -11, -232, -181, -222, -323, -828, -353, -252, -171, -666, -252, -22, -161, -737, -525, -494, -989, -252, -232, -929, -434, -1551, -33, -272, -525, -252, -111, -494, -585, -5775, -656, -252, -989,...
null
A033848_aug
[ 22, 110, 352, 836, 1804, 3740, 6556, 11880, 19624, 30888, 52184, 81466, 124058, 182622, 267806, 384934, 555302, 789558, 1111660 ]
null
A239914_aug
[ 1, 4, 17, 92, 633, 5316, 52609, 598444, 7685705, 109933268, 1732565841, 29824133436, 556682481817, 11198025452260 ]
null
A347287
[ 1, 3, 5, 11, 23, 39, 75, 151, 279, 559, 1071, 2127, 4255, 8351, 16687, 33327, 66095, 132191, 263263, 526511, 1052847, 2101423, 4202847, 8405695, 16794303, 33587903, 67175807, 134284671, 268568959, 537004415, 1074006399, 2148012799, 4295496447, 859099...
[ "nonn", "easy" ]
A012450_aug
[ 4, 42, 210210, 2241915522, 146361182839298, 18963982821764575000, 5.702647873782169e+24 ]
null
A333384_aug
[ 0, 1, 5, 10, 18, 27, 39, 52, 72, 96, 121, 169, 218, 268, 341, 425, 525, 628, 732, 837, 945, 1054, 1164, 1364, 1607, 1851, 2096, 2342, 2615, 3235, 3856, 4502, 5149, 5797, 6450, 7104, 7765, 8429, 9094, 9760, 12415, 15071, 17874, 206...
null
A058713_aug
[ 32, 35, 45, 50, 61, 69, 79, 90, 106, 122, 142, 156, 184, 206, 242, 269, 304, 346, 391, 442, 502, 556, 634, 707, 801, 892, 999, 1114, 1249, 1392, 1555 ]
null
A091296_aug
[ 9, 15, 33, 35, 39, 51, 55, 57, 77, 91, 93, 95, 111, 115, 119, 133, 155, 159, 177, 319, 335, 339, 355, 371, 377, 391, 393, 395, 511, 515, 517, 519, 533, 535, 537, 551, 553, 559, 573, 579, 591, 597, 713, 717, 731, 737, 753, ...
null
A126784_aug
[ 5596, 16400, 44106, 71962, 105614, 144666, 185752, 227444, 271170, 315592, 361586, 409050, 459844, 512306, 567570, 623122, 684908, 747264, 812086, 878330, 945642, 1015606, 1089518, 1169430, 1250002, 1332314, 1416408, 1504450, 1598624, 1693590, 1792786, 1...
null
A051720_aug
[ 5, 5, 4, 4, 7, 10, 7, -2, -1, 50, 2669, -362, -1241, 250, 1517, -43410, -1623811, 276362, 10405295, 21382, -21491075, -32209342, 2523785345, 107638078, -1827648881, -842271806, 11254630553, 17380760743958, -596303510772245 ]
null
A282716_aug
[ 1, -1, 1, -1, 1, -1, 1, -1, 2, -1, 1, -2, 1, 0, 1, -1, 1, -3, 3, 0, 1, -1, 2, -2, 1, -2, 0, -1, 1, -2, 3, -1, 1, 0, 0, -1, 1, -1, 4, -6, 0, -4, 0, 0, 1, -1, 2, -3, 3, -3, 1, -3, 0, 0, 1, -1, 2, -4, 3,...
null
A297516_aug
[ 6, 65, 363, 2610, 19187, 134123, 956810, 6834267, 48617437, 346450092, 2468975717, 17589178379, 125325570606, 892966071949, 6362349116511, 45332105458684, 322993886339549, 2301344223018433, 16397188735256084, 116830761042732200 ]
null
A280618_aug
[ 0, 1, -1, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...
null
A282348_aug
[ -5, 15, 30, 10, 25, 50, 60, 135, 80, 100, 185, 220, 45, 125, 265, 305, 335, 65, 255, 385, 485, 475, 435, 55, 425, 565, 445, 705, 465, 605, 175, 210, 430 ]
null
A327032_aug
[ -4, 0, -27, 12, -95, 53, -252, 159, -558, 382, -1089, 790, -1937, 1467, -3210, 2513, -5032, 4044, -7543, 6192, -10899, 9105, -15272, 12947, -20850, 17898, -27837, 24154, -36453, 31927, -46934, 41445, -59532, 52952, -74515, 66708, -92167, 8298...
null
A136604_aug
[ -25, -68, -86, -127, -145, -185, -209, -248, -266, -312, -329, -367, -394, -432, -456, -499, -517, -556, -579, -616, -639, -682, -707, -743, -775, -811, -836, -880, -905, -940, -974, -1005, -1031, -1068, -1092, -1127, -1159, -1191, -1218, ...
null
A172398_aug
[ 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 0, 1, 1, 0, 1, 1, 1, 1, 2, 1, 0, 0, 1, 1, 2, 1, 0, 0, 1, 0, 1, 1, 0, 0, 2, 1, 1, 0, 0, 1, 2, 0, 1, 1, 0, 0, 3, 1, 0, 0, 1, 0, 1, 0, 0, 1, 2, 0, 1, 1, 1, 0, 2...
null
A313895_aug
[ 4, 20, 40, 64, 84, 108, 132, 148, 168, 188, 208, 232, 256, 280, 300, 320, 340, 356, 376, 400, 424, 448, 472, 492, 508, 528, 548, 568, 592, 616, 640, 660, 680, 700, 716, 740, 764, 784, 808, 828, 848, 868, 888, 912, 932, 956, ...
null
A329526_aug
[ 1, 2, 3, 4, 4, 3, 4, 5, 5, 6, 6, 5, 6, 6, 7, 6, 7, 6, 7, 7, 7, 6, 5, 4, 5, 6, 6, 7, 8, 7, 7, 6, 7, 7, 6, 5, 6, 7, 8, 7, 8, 7, 8, 8, 8, 7, 7, 6, 6, 7, 8, 8, 9, 8, 9, 9, 9, 8, 7, 6, 7, 7, 6, 5...
null
A018063_aug
[ 1, 1, 2, 4, 7, 11, 18, 30, 49, 79, 129, 210, 343, 557, 907, 1476, 2401, 3905, 6352, 10332, 16807, 27337, 44467, 72329, 117649, 191365, 311269, 506304, 823543, 1339555, 2178889, 3544131, 5764801, 9376890, 15252229, 24808919, 40353607, 65638231...
null
A327700_aug
[ 6, 9, 15, 69, 177, 183, 249, 453, 699, 789, 807, 879, 1119, 1203, 1299, 1509, 1623, 1857, 2103, 2913, 3309, 4299, 4479, 4803, 4863, 5583, 5847, 6297, 6537, 7113, 7323, 7629, 8223, 8553, 8709, 8997, 9249, 9543, 9939, 10239, 10677, 1089...
null
A215360
[ 2, 3, 17, 19, 37, 53, 71, 89, 139, 157, 173, 191, 223, 241, 257, 293, 359, 461, 463, 479, 547, 563, 599, 631, 683, 701, 733, 751, 769, 853, 887, 937, 971, 1039, 1091, 1109, 1193, 1277, 1279, 1381, 1447, 1481, 1483, 1499, 1549, ...
[ "nonn", "easy" ]
A077692_aug
[ -3, -122, -123258, -1234808, -123457043, -12345625547, -12345671807243, -123456781852388, -123456789378124020, -12345678910482682000, -1.2345678910110004e+23, -1.2345678910111246e+27 ]
null
A350715_aug
[ 0, 0, 1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0,...
null
A218195_aug
[ 113, 16001, 2081511, 267240217, 34205771911, 4378092248621, 560375293762217, 71725802085285470 ]
null
A275180_aug
[ 41, -256, 317, -482, 1465, -4603, 14643, -46799, 149772, -479722, 1538582, -4942028, 15891866, -51127466, 164489244, -529125544, 1701961499, -5474696445, 17611978722, -56660560468, 182287542046, -586443173365, 1886643497675, -6069534405199 ]
null
A250402_aug
[ 0, 17, 73, 145, 164, 206, 227, 260, 284, 327, 383, 467, 497, 518, 558, 630, 669, 732 ]
null
A137795_aug
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 15, 1, 1, 1, 1, 1, 3, 5, 105, 1, 1, 1, 1155, 1, 15, 1, 1, 1, 1, 35, 15015, 1, 1, 1, 255255, 385, 3, 1, 5, 1, 105, 1, 4849845, 1, 1, 1, 3, 5005, 1155, 1, 1, 7, 15, 85...
null
A028903_aug
[ -9, 8, -7, 6, -5, 4, -3, 2, -1, 0, -1, 0, 1, -2, 3, -4, 5, -6, 7, -8, 7, -8, 9, -10, 11, -12, 13, -14, 15, -16, 15, -16, 17, -18, 19, -20, 21, -22, 23, -24, 23, -24, 25, -26, 27, -28, 29, -30, 31, -32, 31, -32, 3...
null
A291611_aug
[ 1, 3, 6, 16, 30, 33, 36, 37, 85, 288, 561, 805, 850, 1057, 1192, 1312, 2571, 4579, 5223, 5940, 10191, 18756, 24564, 29595, 43891, 65905, 89118, 97963, 112003, 139945, 174101, 195221 ]
null
A257267_aug
[ 2172480, 27453920, 351245245, 3585489039, 36364601876, 321367717120, 2809282726229, 22439783935639, 177308319369825, 1317073010198687, 9691252958920112, 68263746387050580, 477086582631996540 ]
null
A201762_aug
[ 4, -2, 2, -2, -2, 6, -1, -6, 2, 1, 1, -1, 4, -1, -1, 3, -2, -4, -2, 2, 4, 3, -7, 1, 4, -5, 2, -1, 6, -2, -5, -2, 6, -4, -2, 8, -2, -5, 1, 3, -1, 3, 2, -9, 6, -4, 6, -2, -2, -4, 2, 3, -1, -3, 4, 4, -7, -...
null
A096920_aug
[ 1, -1, 1, 1, -1, 2, 0, 0, 2, 1, 1, 0, 2, 1, 3, 2, 0, 4, 2, 2, 4, 4, 2, 5, 5, 4, 6, 6, 6, 7, 9, 6, 10, 10, 10, 14, 12, 12, 16, 16, 16, 20, 20, 21, 25, 26, 24, 32, 32, 32, 38, 39, 41, 46, 50, 50, 56, 60, ...
null
A042428_aug
[ 81, 327, 1716, 2043, 9888, 81147, 91035, 627357, 718392, 6374493, 26216364, 32590857, 189170649, 789273453, 42809937111, 172029021897, 902955046596, 1074984068493, 5202891320568, 42698114633037 ]
null
A090305_aug
[ -2, 16, -258, 4144, -66562, 1069136, -17172738, 275832944, -4430499842, 71163830416, -1143051786498, 18359992414384, -294902930416642, 4736806879080656, -76083812995707140, 1222077814810395000, -19629328849962025000 ]
null
A351473_aug
[ 27, 37, 132, 148, 270, 292, 308, 360, 369, 404, 440, 576, 636, 707, 756, 864, 1295, 1314, 1332, 1365, 1386, 1408, 1480, 1507, 1752, 1896 ]
null
A012399_aug
[ 0, 0, -2, 3, 0, 10, 32, -1596, 10080, -27936, 19008, 4728240, -113762880, 1378522080, -12151639680, 24566643360, 3018767431680, -84947924490240, 1424022331422720, -18489594521756160, 42627235124920320 ]
null
A231768_aug
[ 324, 160000, 32924644, 8871756100, 2161088164096, 543898799003044, 135349381353554400, 33806881984091218000 ]
null
A255493_aug
[ 14, 16, 33648, 34000 ]
null
A067793_aug
[ 1, 25, 35, 49, 55, 65, 77, 85, 91, 95, 115, 119, 121, 125, 133, 143, 145, 155, 161, 169, 175, 185, 187, 203, 205, 209, 215, 217, 221, 235, 245, 247, 253, 259, 265, 275, 287, 289, 295, 299, 301, 305, 319, 323, 325, 329, 335, ...
null
A170681_aug
[ 47, 2302, 108333, 5091836, 239316523, 11247876858, 528650212649, 24846559994872, 1167788319759399, 54886051028692216, 2579644398348535000, 121243286722381120000, 5.698434475951913e+21, 2.678264203697399e+23 ]
null
A145358_aug
[ 1, 7, 49, 421, 3697, 37933, 404341, 4841341, 61291861, 848268421, 12465197269, 197121724549, 3302727019621, 58876330343173, 1107627703783909, 21990846791015844, 458649487144877060, 10035575758396240000, 229687317927141700000, 5.48996602499517e+21 ]
null
A326184_aug
[ 33, 58, 85, 125, 154, 202, 243, 288, 321, 383, 399, 450, 473, 535, 574, 655, 696, 737, 794, 857, 914, 979, 1026, 1095, 1160, 1252, 1303, 1408, 1461, 1551, 1630, 1711, 1768, 1886, 1904, 1982, 2063, 2167, 2230, 2333, 2414, 2536, 2625,...
null
A316531_aug
[ -2, -5, 5, 1, 24, 12, 44 ]
null
A116088_aug
[ 1, 0, 1, 0, 2, 1, 0, 1, 4, 1, 0, 0, 6, 6, 1, 0, 0, 4, 7, 0, 1, 0, 0, 1, 4, 4, 2, 1, 0, 0, 0, 7, 0, 5, 4, 1, 0, 0, 0, 6, 6, 0, 2, 6, 1, 0, 0, 0, 1, 0, 2, 4, 3, 0, 1, 0, 0, 0, 0, 4, 4, 7, 4, 0...
null
A052316_aug
[ 9, 12, 38, 352, 5378, 106460, 2562190, 72592824, 2367054458, 87320153908, 3595646533190, 163492924997456, 8136172620013810, 439858024910227600, 25670670464821310000, 1.608575860476991e+21, 1.0771667511734198e+23 ]
null
A271450_aug
[ 27, 18, 15, 42, 882 ]
null
A182554_aug
[ 377, -323, 1891, -442, 2834, -2737, 4181, -3827, 6479, -5777, 6721, -6601, 10877, -8149, 13201, -11663, 15251, -13981, 17711, -17119, 19043, -18407, 23407, -20999, 27323, -25877, 34561, -30889, 35207, -34943, 40501, -39203, 47519, -44099, 51841, ...
null
A292467_aug
[ 1, 2, 9, 94, 18, 60, 210, 36, 510, 624, 90, 4290, 2604, 2340, 792, 8512, 9324, 3960, 9396, 600, 3600, 7840, 5472, 6840, 5520, 10296, 7800, 6120, 12768, 9450, 18240, 33600, 16200, 37800, 27360, 68796, 222768, 59400, 118944, 156240, 13932...
null
A320655_aug
[ 4, 0, 2, -2, 2, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, -2, 0, 0, 2, -2, 2, -2, 2, 0, 4, 0, 2, 0, 2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, 2, 0, 4, -2, 2, -2, 2, 0, 4, -2, 0, -2, 2, -2, 2,...
null
A333220_aug
[ 0, -6, -12, -24, -30, -48, -96, -60, -192, -384, -120, -768, -108, -126, -1536, -3072, -240, -216, -6144, -480, -12288, -24576, -252, -49152, -408, -960, -98304, -432, -1920 ]
null
A150137_aug
[ 1, 2, 2, 0, 1, 3, 0, 0, 0, 0, 0, 2, 0, 1, 3, 2, 0, 2, 0, 0, 0, 0, 1, 0, 1, 3, 1, 1 ]
null
A199653_aug
[ 122, 14399942995, 1427019681167613000, 1.4140910205960855e+26 ]
null
A383814_aug
[ 2, 37, 373, 19937, 257931013, 4199993923 ]
null
A177037_aug
[ 3, 0, 9, 4, 1, 1, 2, 9, 1, 9, 0, 8, 2, 7, 9, 1, 9, 7, 2, 5, 9, 4, 8, 0, 9, 7, 2, 7, 9, 9, 7, 0, 6, 5, 5, 5, 4, 1, 7, 4, 4, 6, 0, 3, 9, 6, 2, 5, 7, 4, 1, 4, 6, 1, 4, 8, 2 ]
null
A040830_aug
[ 29, 3, 14, 3, 58, 3, 14, 3, 58, 3, 14, 3, 58, 3, 14, 3, 58, 3, 14, 3, 58, 3, 14, 3, 58, 3, 14, 3, 58, 3, 14, 3, 58, 3, 14, 3, 58, 3, 14, 3, 58, 3, 14, 3, 58, 3, 14, 3, 58, 3, 14, 3, 58, 3, 14, 3, 58, 3,...
null
A005734_aug
[ 14, 23, 28, 33, 42, 49, 59, 66, 77, 86, 96, 103, 110 ]
null
A360653_aug
[ 1, 1, 1, 2, 1, 3, 1, 4, 1, 3, 5, 1, 6, 1, 7, 1, 8, 1, 4, 6, 9, 1, 10, 1, 11, 1, 12, 1, 13, 1, 5, 10, 14, 1, 15, 1, 16, 1, 17, 1, 18, 1, 10, 19, 1, 6, 15, 20, 1, 21, 1, 22, 1, 23, 1, 24, 1, 25, 1, 26...
null
A192190_aug
[ 0, 2, 2, 2, 4, 2, 6, 4, 2, 2, 8, 2, 2, 6, 4, 2, 6, 2, 2, 10, 4, 2, 8, 2, 4, 2, 8, 2, 10, 2, 6, 4, 2, 2, 12, 4, 2, 4, 2, 2, 4, 2, 4, 2, 6, 2, 6, 12, 2, 2, 2, 4, 2, 2, 2, 4, 4, 6, 2, 10, 4, 2, 2...
null
A222250_aug
[ 0, 1, 2, 3, 4, 5, 8, 7, 6, 9, 10, 11, 12, 13, 14, 15, 18, 17, 16, 19, 20, 21, 22, 23, 24, 25, 28, 27, 26, 29, 30, 31, 32, 33, 34, 35, 38, 37, 36, 39, 40, 41, 42, 43, 44, 45, 48, 47, 46, 49, 50, 51, 52, 53, 54...
null
A322802_aug
[ 1, -1, 1, -1, 1, -1, 1, -2, 3, -4, 0, -1, 2, -3, 0, -3, 2, -2, 3, -1, 0, -1, 0, -3, 1, 0, 3, -1, 1, -1, 0, -3, 1, -4, 3, -1, 4, -3, 3, 0, 1, 0, 0, -1, 1, 0, 0, -2, 4, -1, 3, 0, 2, -2 ]
null
A318662_aug
[ 1, 1, 2, 1, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 4, 2, 2, 8, 2, 2, 4, 2, 2, 4, 8, 2, 16, 2, 2, 4, 2, 2, 4, 2, 4, 8, 2, 2, 4, 4, 2, 4, 2, 2, 16, 2, 2, 4, 8, 8, 4, 2, 2, 16, 4, 4, 4, 2, 2, 4, 2, 2, 16,...
null
A188303_aug
[ 128, 3656, 317912, 53147004, 21562300728 ]
null
A223990_aug
[ 56, 3136, 99634, 2086196, 31831914, 378122264, 3661410444, 29889154034, 211009204916, 1314178222276, 7336228725354, 37185201981670, 172974779780114, 745060738789758, 2994209711354545, 11299608627412728, 40267814207071510 ]
null
A122302_aug
[ 0, 12, 28, 24, 16, 72, 88, 64, 60, 52, 44, 36, 184, 200, 216, 244, 256, 248, 232, 188, 240, 172, 160, 128, 136, 140, 204, 120, 152, 104, 148, 100, 92, 520, 536 ]
null
A070305_aug
[ -2, -6, -14, -24, -35, -49, -65, -88, -115, -143, -172, -203, -235, -273, -320, -373, -432, -496, -563, -634, -713, -796, -882, -982, -1085, -1192, -1306, -1431, -1558, -1686, -1817, -1953, -2090, -2229, -2376, -2525, -2676, -2843, -3013, ...
null
A026662_aug
[ 1, 8, 38, 202, 873, 4228, 17982, 83986, 356720, 1636710, 6967782, 31651902, 135174069, 610281684, 2614576678, 11756749378, 50516489196, 226522941742, 975898078974, 4367362698334, 18859586883256, 84276937119086, 364693906704798 ]
null
A313884_aug
[ 1, 5, 10, 16, 21, 27, 31, 35, 41, 46, 52, 57, 62, 67, 72, 78, 83, 89, 93, 97, 103, 108, 114, 119, 124, 129, 134, 140, 145, 151, 155, 159, 165, 170, 176, 181, 186, 191, 196, 202, 207, 213, 217, 221, 227, 232, 238, 243, 24...
null
A369813_aug
[ -1, 0, -1, 0, -1, 0, -1, -1, -1, -2, -1, -3, -1, -4, -2, -5, -4, -6, -7, -7, -11, -9, -16, -13, -22, -20, -29, -31, -38, -47, -51, -69, -71, -98, -102, -136, -149, -187, -218, -258, -316, -360, -452, -509, -639, -727, -897, ...
null
A196058_aug
[ 0, -5, 10, -10, 15, -15, 10, -10, 20, -20, 20, -15, 15, -15, 25, -10, 15, -20, 10, -20, 20, -25, 20, -15, 30, -20, 20, -15, 20, -25, 25, -10, 30, -20, 25, -20, 15, -15, 25, -20, 20, -20, 15, -25, 25, -20, 25, -15, 20, ...
null
A251825_aug
[ 6, 4, 6, 8, 8, 6, 8, 2, 4 ]
null
A371744_aug
[ -1, -5, -4, -1, -1, -1, -1, 0, -4, -2, -5, -3, -1, -1, -5, -5, -1, -3, -4, -1 ]
null
A125591_aug
[ 0, 0, 0, 1, 304, 12883, 305373, 4626271, 49074852, 414408128, 3190286294, 24698286376 ]
null
A331556_aug
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A060519
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[ "nonn" ]
A251953_aug
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A134050_aug
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A133175_aug
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A015830_aug
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A312881_aug
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A314407_aug
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A175834_aug
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A377033_aug
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A191043_aug
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A045914_aug
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A322515
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[ "nonn", "base" ]
A368427_aug
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A030940_aug
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A107668_aug
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A214686_aug
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A111530_aug
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A271760_aug
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A054774_aug
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A181675_aug
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A387261_aug
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A295980
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[ "nonn" ]
A094572_aug
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A090848_aug
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