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amenable n.  and  heptagonal n.

First numbers that belong to both sets:

1, 81, 112, 148, 189, 469, 540, 616, 697, 1177, 1288, 1404, 1525, 2205, 2356, 2512, 2673, 3553, 3744, 3940, 4141, 5221, 5452, 5688, 5929, 7209, 7480, 7756, 8037, 9517, 9828, 10144, 10465, 12145, 12496, 12852, 13213, 15093, 15484, 15880, 16281, 18361, 18792, 19228, 19669, 21949, 22420, 22896, 23377, 25857, 26368, 26884, 27405, 30085, 30636, 31192, 31753, 34633, 35224, 35820, 36421, 39501, 40132, 40768, 41409, 44689, 45360, 46036, 46717, 50197, 50908, 51624, 52345, 56025, 56776, 57532, 58293, 62173, 62964, 63760, 64561, 68641, 69472, 70308, 71149, 75429, 76300, 77176, 78057, 82537, 83448, 84364, 85285, 89965, 90916, 91872, 92833, 97713, 98704, 99700, 100701, 105781, 106812, 107848, 108889, 114169, 115240, 116316, 117397, 122877, 123988, 125104, 126225, 131905, 133056, 134212, 135373, 141253, 142444, 143640, 144841, 150921, 152152, 153388, 154629, 160909, 162180, 163456, 164737, 171217, 172528, 173844, 175165, 181845, 183196, 184552, 185913, 192793, 194184, 195580, 196981, 204061, 205492, 206928, 208369, 215649, 217120, 218596, 220077, 227557, 229068, 230584, 232105, 239785, 241336, 242892, 244453, 252333, 253924, 255520, 257121, 265201, 266832, 268468, 270109, 278389, 280060, 281736, 283417, 291897, 293608, 295324, 297045, 305725, 307476, 309232, 310993, 319873, 321664, 323460, 325261, 334341, 336172, 338008, 339849, 349129, 351000, 352876, 354757, 364237, 366148, 368064, 369985, 379665, 381616, 383572, 385533, 395413, 397404, 399400, 401401, 411481, 413512, 415548, 417589, 427869, 429940, 432016, 434097, 444577, 446688, 448804, 450925, 461605, 463756, 465912, 468073, 478953, 481144, 483340, 485541, 496621, 498852, 501088, 503329, 514609, 516880, 519156, 521437, 532917, 535228, 537544, 539865, 551545, 553896, 556252, 558613, 570493, 572884, 575280, 577681, 589761, 592192, 594628, 597069, 609349, 611820, 614296, 616777, 629257, 631768, 634284, 636805, 649485, 652036, 654592, 657153, 670033, 672624, 675220, 677821, 690901, 693532, 696168, 698809, 712089, 714760, 717436, 720117, 733597, 736308, 739024, 741745, 755425, 758176, 760932, 763693, 777573, 780364, 783160.

Some larger examples :