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happy n.  and  Lehmer n.

First numbers that belong to both sets:

91, 133, 763, 1141, 1285, 2091, 3031, 3097, 3367, 3667, 6643, 8245, 11041, 12801, 14911, 15211, 16441, 16471, 22261, 23281, 26281, 27223, 28231, 28939, 33001, 39491, 44317, 44941, 47989, 49987, 52429, 52507, 52801, 53983, 55423, 55537, 57205, 62745, 63631, 68251, 69751, 73555, 79003, 82411, 83293, 88561, 92833, 93031, 93961, 96139, 101311, 111361, 113401, 113611, 114589, 125563, 126701, 136981, 137311, 137971, 140911, 141661, 146611, 147259, 148291, 149443, 159757, 160147, 163891, 164041, 164761, 186961, 187867, 190411, 193249, 196093, 197011, 205543, 206521, 208273, 212323, 213265, 215611, 216651, 220405, 221371, 223231, 225589, 226081, 226801, 229585, 236215, 237817, 243991, 245791, 248005, 252361, 252601, 255067, 260221, 261289, 263245, 267871, 268135, 272163, 272323, 282133, 289807, 292861, 294847, 303901, 307063, 311491, 312721, 318553, 326599, 328021, 333697, 337441, 344641, 346179, 348781, 350227, 367003, 377233, 377881, 386191, 391141, 399931, 401191, 407431, 425971, 430111, 437431, 439291, 443713, 446431, 446755, 449401, 455533, 458989, 459781, 464101, 475707, 501145, 509671, 512635, 520801, 538135, 550639, 568429, 568711, 575719, 579481, 581077, 586249, 586747, 601441, 601885, 604117, 613711, 614107, 618085, 630631, 637585, 645569, 656635, 658357, 658711, 658801, 670033, 677821, 682021, 682201, 687511, 707851, 714883, 724951, 725551, 731071, 731971, 732351, 737191, 744031, 748657, 749521, 755503, 771001, 792485, 795481, 800299, 802123, 819541, 821401, 842023, 860693, 868105, 868981, 873181, 875161, 877429, 878461, 890947, 892039, 897541, 906193, 906661, 930385, 948157, 954271, 997393, 1008577, 1015201, 1018249, 1019131, 1028041, 1058583, 1060885, 1064701, 1070191, 1077805, 1082401, 1084201, 1092547, 1106785, 1122769, 1145005, 1146613, 1150261, 1170313, 1170331, 1173061, 1208605, 1218151, 1222663, 1224721, 1239491, 1240891, 1241983, 1242571, 1248091, 1249249, 1260805, 1262791, 1269841, 1273741, 1298761, 1305651, 1309111, 1310491, 1311091, 1317331, 1317661, 1341001, 1352851, 1353451, 1364595, 1397851, 1405501, 1411477, 1420579, 1433407, 1436791, 1447693, 1455133, 1460611, 1488169, 1490587, 1496881, 1532635, 1533085, 1535821, 1554991, 1564171, 1604401, 1605253, 1607095, 1610869, 1618219, 1620235.

Some larger examples :