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Cunningham n.  and  untouchable n.

First numbers that belong to both sets:

5, 120, 124, 288, 290, 342, 530, 624, 626, 1332, 1522, 1680, 1682, 2024, 2196, 2198, 2600, 2602, 2808, 3126, 4224, 4488, 4490, 4914, 5328, 6240, 6562, 7568, 8280, 9024, 9026, 9408, 9800, 11024, 11880, 12168, 12320, 13224, 13226, 15128, 15624, 16642, 16806, 17688, 18770, 19880, 20448, 20450, 21608, 22200, 22800, 22802, 23408, 23410, 24388, 24390, 25282, 26568, 30624, 32040, 32760, 34968, 34970, 35720, 37250, 39602, 40400, 41208, 42848, 43682, 45368, 46226, 47962, 48842, 51530, 52440, 58080, 58082, 59048, 59320, 60024, 62000, 63000, 68120, 68922, 69168, 69170, 72360, 73440, 73442, 75626, 76728, 78126, 78960, 78962, 79508, 82368, 83520, 83522, 84680, 84682, 87024, 88208, 93026, 94248, 100488, 101760, 103040, 103822, 106928, 106930, 108240, 109560, 114920, 119024, 123200, 124608, 124610, 130320, 130322, 131768, 140626, 142128, 142130, 143640, 145160, 148878, 151320, 156024, 157608, 160802, 162408, 166374, 167280, 167282, 168922, 173888, 173890, 175560, 187488, 192720, 198024, 198026, 203400, 205208, 208848, 208850, 212520, 212522, 214370, 216224, 221840, 223728, 223730, 226980, 226982, 227528, 229440, 229442, 233288, 235224, 243048, 253008, 259082, 261120, 265224, 267288, 269360, 271440, 274626, 279840, 279842, 284088, 286226, 288368, 294850, 299208, 299210, 301400, 301402, 303600, 303602, 310248, 312480, 321488, 328508, 332928, 332930, 337560, 346922, 349282, 351648, 358800, 358802, 361202, 363608, 366024, 373320, 375770, 380688, 383160, 388128, 390624, 393128, 398160, 400690, 403224, 408320, 408322, 410880, 418608, 421874, 429024, 429026, 431648, 434280, 436920, 442224, 452928, 455624, 456534, 461042, 463760, 463762, 466488, 469224, 469226, 471968, 477480, 480248, 483024, 485808, 485810, 488600, 488602, 491400, 491402, 494208, 494210, 502680, 505520, 505522, 519840, 519842, 522728, 525624, 534360, 534362, 540224, 543168, 543170, 546120, 549080, 555026, 561000, 570024, 570026, 576080, 591360, 597528, 603728, 609960, 613088, 614124, 632024, 638400, 644808, 648024, 654482, 658504, 660968, 664224, 670760, 674040, 683928, 690560, 690562, 693890, 697224, 700568.

Some larger examples :