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amenable n.  and  centered heptagonal n.

First numbers that belong to both sets:

1, 8, 148, 197, 253, 316, 736, 841, 953, 1072, 1772, 1933, 2101, 2276, 3256, 3473, 3697, 3928, 5188, 5461, 5741, 6028, 7568, 7897, 8233, 8576, 10396, 10781, 11173, 11572, 13672, 14113, 14561, 15016, 17396, 17893, 18397, 18908, 21568, 22121, 22681, 23248, 26188, 26797, 27413, 28036, 31256, 31921, 32593, 33272, 36772, 37493, 38221, 38956, 42736, 43513, 44297, 45088, 49148, 49981, 50821, 51668, 56008, 56897, 57793, 58696, 63316, 64261, 65213, 66172, 71072, 72073, 73081, 74096, 79276, 80333, 81397, 82468, 87928, 89041, 90161, 91288, 97028, 98197, 99373, 100556, 106576, 107801, 109033, 110272, 116572, 117853, 119141, 120436, 127016, 128353, 129697, 131048, 137908, 139301, 140701, 142108, 149248, 150697, 152153, 153616, 161036, 162541, 164053, 165572, 173272, 174833, 176401, 177976, 185956, 187573, 189197, 190828, 199088, 200761, 202441, 204128, 212668, 214397, 216133, 217876, 226696, 228481, 230273, 232072, 241172, 243013, 244861, 246716, 256096, 257993, 259897, 261808, 271468, 273421, 275381, 277348, 287288, 289297, 291313, 293336, 303556, 305621, 307693, 309772, 320272, 322393, 324521, 326656, 337436, 339613, 341797, 343988, 355048, 357281, 359521, 361768, 373108, 375397, 377693, 379996, 391616, 393961, 396313, 398672, 410572, 412973, 415381, 417796, 429976, 432433, 434897, 437368, 449828, 452341, 454861, 457388, 470128, 472697, 475273, 477856, 490876, 493501, 496133, 498772, 512072, 514753, 517441, 520136, 533716, 536453, 539197, 541948, 555808, 558601, 561401, 564208, 578348, 581197, 584053, 586916, 601336, 604241, 607153, 610072, 624772, 627733, 630701, 633676, 648656, 651673, 654697, 657728, 672988, 676061, 679141, 682228, 697768, 700897, 704033, 707176, 722996, 726181, 729373, 732572, 748672, 751913, 755161, 758416, 774796, 778093, 781397, 784708, 801368, 804721, 808081, 811448, 828388, 831797, 835213, 838636, 855856, 859321, 862793, 866272, 883772, 887293, 890821, 894356, 912136, 915713, 919297, 922888, 940948, 944581, 948221, 951868, 970208, 973897, 977593, 981296, 999916, 1003661, 1007413, 1011172, 1030072, 1033873, 1037681, 1041496, 1060676, 1064533, 1068397, 1072268, 1091728, 1095641.

Some larger examples :