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pronic n.  and  untouchable n.

First numbers that belong to both sets:

2, 210, 306, 342, 552, 756, 1332, 1406, 1806, 3306, 3422, 4032, 4830, 5256, 5700, 6006, 6480, 6642, 7140, 8190, 8556, 9120, 9702, 10506, 10920, 11130, 11342, 11556, 11772, 12210, 12432, 13572, 13806, 14280, 16770, 17556, 17822, 18906, 20592, 21462, 21756, 22650, 22952, 24806, 26406, 27390, 28056, 29070, 30102, 30800, 31506, 33306, 33672, 36290, 37056, 37830, 40200, 40602, 43056, 43472, 44310, 45156, 45582, 46872, 49062, 49506, 50400, 52212, 54990, 57360, 58806, 59292, 60270, 63756, 64262, 64770, 65280, 66306, 68382, 72630, 73170, 74256, 74802, 75900, 76452, 77562, 78120, 78680, 79806, 82656, 83810, 85556, 86142, 90300, 91506, 95172, 97032, 98282, 99540, 100806, 101442, 105950, 107256, 108570, 111222, 111890, 115940, 116622, 117306, 118680, 119370, 120062, 120756, 124256, 124962, 127092, 127806, 132132, 135056, 135792, 136530, 137270, 141000, 144020, 145542, 146306, 147072, 147840, 151710, 154056, 159600, 162006, 163620, 166056, 168510, 169332, 170982, 171810, 172640, 174306, 180200, 181050, 181902, 182756, 184470, 188790, 189660, 193160, 194922, 195806, 196692, 199362, 200256, 204756, 210222, 211140, 213906, 227052, 228006, 230880, 232806, 234740, 235710, 237656, 238632, 239610, 241572, 242556, 247506, 252506, 257556, 262656, 263682, 266772, 270920, 271962, 273006, 274052, 275100, 278256, 285690, 286760, 288906, 289982, 291060, 295392, 299756, 305256, 309692, 317532, 318660, 322056, 325470, 331200, 339306, 340472, 341640, 357006, 359400, 364212, 371490, 375156, 376382, 378840, 381306, 385020, 386262, 392502, 395012, 398792, 400056, 403860, 405132, 411522, 412806, 416670, 423150, 425756, 427062, 432306, 436260, 437582, 438906, 442890, 444222, 445556, 448230, 450912, 452256, 454950, 459006, 460362, 463080, 465806, 475410, 476790, 485112, 487902, 492102, 493506, 494912, 496320, 500556, 504810, 507656, 509082, 510510, 516242, 517680, 522006, 526350, 527802, 529256, 533630, 535092, 539490, 542432, 545382, 548340, 551306, 558756, 566256, 570780, 573806, 575322, 576840, 581406, 593670, 596756, 598302, 599850, 612306, 613872, 617010, 620156, 624890, 626472, 628056, 632820, 634412.

Some larger examples :