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nude n.  and  sphenic n.

First numbers that belong to both sets:

66, 222, 366, 555, 777, 1113, 1131, 1222, 1266, 1311, 1335, 1362, 1515, 1626, 1662, 1771, 2222, 3111, 3126, 3171, 3333, 5555, 6126, 6366, 7777, 11122, 11155, 11166, 11222, 11226, 11262, 11355, 11535, 12162, 12666, 13155, 13326, 13713, 15135, 15155, 15315, 15515, 15715, 16122, 16266, 16662, 17122, 17171, 21122, 21162, 22222, 22362, 23262, 31335, 31362, 31731, 32322, 32622, 33126, 33162, 33315, 33333, 33555, 35115, 35355, 36222, 37317, 51155, 53115, 53355, 55115, 55155, 55515, 55555, 61266, 61626, 66162, 73311, 73731, 77133, 77777, 111115, 111122, 111126, 112222, 113115, 113133, 113313, 113331, 116322, 122222, 123126, 123666, 126366, 131115, 131226, 131622, 132162, 132222, 132666, 133131, 133311, 133626, 133662, 136326, 136362, 136662, 151555, 155355, 155515, 155535, 155555, 161166, 162366, 163266, 163626, 163662, 171115, 173733, 211222, 211326, 211362, 212122, 212222, 212622, 213126, 213162, 213222, 216222, 216366, 221222, 221226, 221262, 221322, 222126, 222366, 223662, 227122, 231366, 231666, 232266, 233166, 236226, 262266, 262326, 262662, 266226, 271222, 311133, 311226, 311313, 311331, 312126, 312162, 313311, 316266, 316326, 316362, 321162, 321666, 322662, 323166, 323322, 326166, 326226, 326262, 326622, 331131, 331737, 333111, 335535, 353355, 355155, 355335, 361626, 363126, 363162, 363666, 366162, 511115, 515155, 515535, 515555, 531555, 533535, 535155, 551515, 553155, 553515, 555115, 555315, 575155, 612366, 621366, 622122, 631266, 631362, 631662, 632166, 632622, 633162, 661326, 662622, 663162, 712222, 733173, 737331, 757715, 1111115, 1111155, 1111326, 1111515, 1112122, 1112222, 1112226, 1113135, 1113162, 1113333, 1115155, 1115355, 1115555, 1116222, 1117137, 1121222, 1121226, 1121262, 1122162, 1122666, 1123266, 1123662, 1126122, 1126266, 1126326, 1131162, 1131555, 1131711, 1132122, 1132266, 1133115, 1133166, 1133355, 1135335, 1136166, 1136262, 1136622, 1137171, 1151355, 1155515, 1157555, 1162362, 1162626, 1163166, 1163226, 1163262, 1163622, 1166226, 1166262, 1177113, 1211122, 1211222, 1211622, 1212122, 1212126, 1212366, 1213122, 1213662, 1216662, 1221122, 1222626, 1226166, 1226226, 1226262, 1226622, 1231122, 1231266, 1233222, 1236126, 1236162, 1261122, 1261662.

Some larger examples :