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Cunningham n.  and  sphenic n.

First numbers that belong to both sets:

170, 195, 255, 290, 399, 442, 483, 530, 730, 962, 1001, 1023, 1090, 1295, 1370, 1443, 1599, 1729, 2198, 2703, 2810, 2915, 3026, 3126, 3363, 3374, 3970, 4355, 4490, 4623, 4899, 5185, 5626, 5930, 6083, 6562, 7055, 7570, 7743, 7777, 7922, 8099, 8282, 9215, 9262, 9410, 9605, 10610, 11026, 11882, 12099, 12322, 12543, 12545, 12770, 12995, 13226, 14162, 14885, 15626, 16130, 16383, 16385, 16642, 16806, 16899, 17423, 18226, 18770, 19045, 19599, 19682, 20165, 21610, 21905, 22202, 22802, 23410, 24026, 24335, 24963, 25922, 26243, 26245, 26570, 27001, 27890, 29585, 30277, 31683, 32042, 32767, 33123, 34226, 35722, 36865, 38810, 39305, 39999, 40001, 43265, 44099, 44522, 44943, 44945, 46226, 46657, 49283, 49730, 50626, 51530, 51985, 52442, 54755, 55226, 56643, 58082, 61010, 62002, 62499, 63503, 63505, 64001, 66563, 67082, 69170, 69695, 71290, 71823, 72362, 74087, 76730, 78962, 80090, 81226, 82370, 82945, 84682, 85183, 85263, 86435, 86437, 87026, 88210, 90602, 91810, 93026, 93635, 94863, 96099, 96722, 97337, 101123, 103685, 104330, 108899, 109562, 110591, 112895, 112897, 114243, 114245, 114922, 116282, 116965, 120410, 121105, 123202, 125315, 126026, 128882, 129601, 130322, 131770, 133226, 133955, 134690, 136162, 138383, 138385, 139130, 140609, 142883, 144399, 145162, 145923, 146690, 148226, 151322, 152099, 153665, 155237, 156815, 157610, 158405, 161603, 166463, 168099, 169745, 173890, 174723, 175562, 177146, 182330, 184042, 185762, 187490, 191843, 192722, 195365, 197135, 200703, 200705, 202499, 202501, 204305, 205210, 205378, 207026, 211601, 215999, 216226, 219023, 219962, 222785, 225626, 226577, 229442, 230399, 231362, 235226, 236195, 238143, 240099, 241082, 242063, 245026, 248003, 248005, 249999, 251002, 252003, 252005, 253010, 254015, 255026, 259082, 260099, 261122, 263170, 267290, 270399, 274577, 275626, 277730, 278785, 281962, 284090, 287495, 287497, 288370, 290522, 292682, 293763, 293765, 298115, 299210, 300305, 301402, 303602, 304705, 308026, 311363, 313601, 314722, 315845, 318095, 327183, 328330, 334083.

Some larger examples :