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nonagonal n.  and  pernicious n.

First numbers that belong to both sets:

9, 24, 261, 651, 750, 856, 1089, 1216, 1350, 1491, 1639, 2125, 3286, 4446, 4699, 5781, 6364, 6666, 8281, 9334, 12450, 12871, 14176, 16975, 18469, 20559, 21646, 23329, 23904, 25671, 26274, 26884, 28125, 30691, 32016, 32689, 39061, 43624, 47619, 48439, 50941, 53506, 55251, 60654, 65349, 66309, 67276, 68250, 70219, 73225, 79426, 88086, 90321, 97194, 104319, 110449, 111696, 120621, 129889, 131241, 135339, 139500, 145146, 148011, 159751, 171939, 182971, 187804, 194346, 197659, 202681, 216381, 235950, 241434, 245125, 250714, 252591, 262081, 264000, 269799, 273700, 277629, 283575, 295656, 305916, 310069, 316351, 324825, 326961, 331254, 339924, 346500, 348706, 350919, 353139, 359841, 373434, 380325, 382636, 389611, 410914, 415725, 445179, 447679, 450186, 455221, 457749, 460284, 465375, 470494, 475641, 488631, 496509, 499149, 512454, 517825, 520521, 531375, 542341, 545100, 556206, 561801, 567424, 573075, 590196, 595959, 619291, 628156, 655129, 670359, 682669, 695091, 698214, 704481, 713934, 717099, 723450, 736236, 742671, 745899, 752376, 755625, 762144, 765414, 768691, 781869, 788500, 791826, 805200, 822075, 849439, 866769, 891325, 898404, 905511, 909075, 912646, 930606, 959706, 963375, 996711, 1000450, 1007949, 1011709, 1023031, 1026819, 1038225, 1045864, 1049694, 1065084, 1072821, 1076700, 1092286, 1096200, 1111926, 1151731, 1163809, 1167849, 1175950, 1196325, 1241766, 1258500, 1279575, 1288054, 1313659, 1317951, 1330869, 1348191, 1352539, 1356894, 1370001, 1387575, 1396404, 1405261, 1414146, 1423059, 1436481, 1440969, 1458991, 1463514, 1495371, 1504536, 1522950, 1532199, 1536834, 1546125, 1564791, 1569475, 1574166, 1616700, 1621461, 1640575, 1654984, 1659801, 1664625, 1683991, 1698589, 1708356, 1723059, 1727974, 1752654, 1767546, 1777509, 1787500, 1812600, 1827744, 1842951, 1863325, 1883811, 1894096, 1904409, 1930314, 1951164, 1972126, 1987921, 2003779, 2014386, 2035684, 2051731, 2067841, 2073225, 2132911, 2138379, 2143854, 2165824, 2176851, 2182375, 2187906, 2198989, 2226819, 2232406, 2238000, 2249209, 2254824, 2271711, 2283004, 2334169, 2362839, 2368594, 2385901, 2432361, 2455759, 2461626, 2467500, 2473381, 2479269, 2485164, 2502891, 2538534, 2544499, 2550471, 2556450, 2574429, 2586450, 2610576, 2616625, 2628744, 2640891, 2646975, 2653066.

Some larger examples :