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amenable n.  and  centered nonagonal n.

First numbers that belong to both sets:

1, 28, 136, 253, 325, 496, 820, 1081, 1225, 1540, 2080, 2485, 2701, 3160, 3916, 4465, 4753, 5356, 6328, 7021, 7381, 8128, 9316, 10153, 10585, 11476, 12880, 13861, 14365, 15400, 17020, 18145, 18721, 19900, 21736, 23005, 23653, 24976, 27028, 28441, 29161, 30628, 32896, 34453, 35245, 36856, 39340, 41041, 41905, 43660, 46360, 48205, 49141, 51040, 53956, 55945, 56953, 58996, 62128, 64261, 65341, 67528, 70876, 73153, 74305, 76636, 80200, 82621, 83845, 86320, 90100, 92665, 93961, 96580, 100576, 103285, 104653, 107416, 111628, 114481, 115921, 118828, 123256, 126253, 127765, 130816, 135460, 138601, 140185, 143380, 148240, 151525, 153181, 156520, 161596, 165025, 166753, 170236, 175528, 179101, 180901, 184528, 190036, 193753, 195625, 199396, 205120, 208981, 210925, 214840, 220780, 224785, 226801, 230860, 237016, 241165, 243253, 247456, 253828, 258121, 260281, 264628, 271216, 275653, 277885, 282376, 289180, 293761, 296065, 300700, 307720, 312445, 314821, 319600, 326836, 331705, 334153, 339076, 346528, 351541, 354061, 359128, 366796, 371953, 374545, 379756, 387640, 392941, 395605, 400960, 409060, 414505, 417241, 422740, 431056, 436645, 439453, 445096, 453628, 459361, 462241, 468028, 476776, 482653, 485605, 491536, 500500, 506521, 509545, 515620, 524800, 530965, 534061, 540280, 549676, 555985, 559153, 565516, 575128, 581581, 584821, 591328, 601156, 607753, 611065, 617716, 627760, 634501, 637885, 644680, 654940, 661825, 665281, 672220, 682696, 689725, 693253, 700336, 711028, 718201, 721801, 729028, 739936, 747253, 750925, 758296, 769420, 776881, 780625, 788140, 799480, 807085, 810901, 818560, 830116, 837865, 841753, 849556, 861328, 869221, 873181, 881128, 893116, 901153, 905185, 913276, 925480, 933661, 937765, 946000, 958420, 966745, 970921, 979300, 991936, 1000405, 1004653, 1013176, 1026028, 1034641, 1038961, 1047628, 1060696, 1069453, 1073845, 1082656, 1095940, 1104841, 1109305, 1118260, 1131760, 1140805, 1145341, 1154440, 1168156, 1177345, 1181953, 1191196, 1205128, 1214461, 1219141, 1228528, 1242676, 1252153, 1256905, 1266436, 1280800, 1290421, 1295245, 1304920, 1319500, 1329265, 1334161, 1343980, 1358776, 1368685, 1373653, 1383616, 1398628, 1408681.

Some larger examples :