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amenable n.  and  decagonal n.

First numbers that belong to both sets:

1, 52, 85, 232, 297, 540, 637, 976, 1105, 1540, 1701, 2232, 2425, 3052, 3277, 4000, 4257, 5076, 5365, 6280, 6601, 7612, 7965, 9072, 9457, 10660, 11077, 12376, 12825, 14220, 14701, 16192, 16705, 18292, 18837, 20520, 21097, 22876, 23485, 25360, 26001, 27972, 28645, 30712, 31417, 33580, 34317, 36576, 37345, 39700, 40501, 42952, 43785, 46332, 47197, 49840, 50737, 53476, 54405, 57240, 58201, 61132, 62125, 65152, 66177, 69300, 70357, 73576, 74665, 77980, 79101, 82512, 83665, 87172, 88357, 91960, 93177, 96876, 98125, 101920, 103201, 107092, 108405, 112392, 113737, 117820, 119197, 123376, 124785, 129060, 130501, 134872, 136345, 140812, 142317, 146880, 148417, 153076, 154645, 159400, 161001, 165852, 167485, 172432, 174097, 179140, 180837, 185976, 187705, 192940, 194701, 200032, 201825, 207252, 209077, 214600, 216457, 222076, 223965, 229680, 231601, 237412, 239365, 245272, 247257, 253260, 255277, 261376, 263425, 269620, 271701, 277992, 280105, 286492, 288637, 295120, 297297, 303876, 306085, 312760, 315001, 321772, 324045, 330912, 333217, 340180, 342517, 349576, 351945, 359100, 361501, 368752, 371185, 378532, 380997, 388440, 390937, 398476, 401005, 408640, 411201, 418932, 421525, 429352, 431977, 439900, 442557, 450576, 453265, 461380, 464101, 472312, 475065, 483372, 486157, 494560, 497377, 505876, 508725, 517320, 520201, 528892, 531805, 540592, 543537, 552420, 555397, 564376, 567385, 576460, 579501, 588672, 591745, 601012, 604117, 613480, 616617, 626076, 629245, 638800, 642001, 651652, 654885, 664632, 667897, 677740, 681037, 690976, 694305, 704340, 707701, 717832, 721225, 731452, 734877, 745200, 748657, 759076, 762565, 773080, 776601, 787212, 790765, 801472, 805057, 815860, 819477, 830376, 834025, 845020, 848701, 859792, 863505, 874692, 878437, 889720, 893497, 904876, 908685, 920160, 924001, 935572, 939445, 951112, 955017, 966780, 970717, 982576, 986545, 998500, 1002501, 1014552, 1018585, 1030732, 1034797, 1047040, 1051137, 1063476, 1067605, 1080040, 1084201, 1096732, 1100925, 1113552, 1117777, 1130500, 1134757, 1147576, 1151865, 1164780, 1169101, 1182112, 1186465, 1199572, 1203957, 1217160, 1221577, 1234876, 1239325, 1252720.

Some larger examples :