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gapful n.  and  Lehmer n.

First numbers that belong to both sets:

451, 561, 1111, 1695, 1729, 3367, 4141, 5151, 8245, 13107, 13651, 13981, 14833, 17563, 17611, 22359, 34441, 35371, 37231, 39091, 39865, 41041, 45551, 56661, 67771, 69601, 80665, 85765, 101101, 104923, 108691, 113201, 114589, 120289, 122221, 129795, 131461, 134539, 135679, 136741, 140811, 142519, 142681, 145027, 148291, 153349, 157641, 167713, 167761, 168103, 168421, 176011, 176149, 180851, 182533, 187867, 189943, 193249, 195315, 245659, 301351, 319021, 332815, 342271, 343315, 348781, 355291, 399001, 399931, 410041, 449401, 489991, 524841, 609451, 614941, 618085, 627751, 630565, 637585, 638731, 686311, 730661, 780361, 812659, 825265, 843115, 849745, 864535, 868105, 881365, 898705, 903355, 931855, 936481, 954577, 1004653, 1006621, 1008349, 1011517, 1015201, 1031953, 1044667, 1045815, 1049959, 1063051, 1064701, 1074271, 1079143, 1089673, 1097041, 1107161, 1113211, 1113463, 1118821, 1139281, 1140547, 1146613, 1157101, 1157689, 1158829, 1168597, 1189609, 1195381, 1218151, 1221883, 1222663, 1224091, 1230853, 1239491, 1242241, 1242571, 1247233, 1267651, 1272271, 1272821, 1276231, 1315171, 1316719, 1317823, 1326795, 1328041, 1334311, 1353451, 1364341, 1364595, 1366981, 1367497, 1377103, 1400971, 1406209, 1406581, 1410871, 1447693, 1453933, 1461031, 1493701, 1498981, 1500961, 1508239, 1517131, 1569457, 1571361, 1592599, 1602601, 1605253, 1612171, 1625261, 1645391, 1659361, 1664419, 1672231, 1677403, 1699291, 1716859, 1718431, 1720335, 1730311, 1737571, 1760011, 1769377, 1769801, 1773289, 1778711, 1785829, 1786969, 1798939, 1800931, 1802251, 1804451, 1822879, 1824043, 1825681, 1827001, 1855381, 1857031, 1859341, 1891777, 1896973, 1900515, 1907851, 1909831, 1910821, 1932463, 1937881, 1965379, 1971541, 1977151, 1987381, 2480689, 2632939, 2884223, 3035551, 3065311, 3071407, 3101377, 3120181, 3130645, 3134131, 3146221, 3181465, 3206671, 3214111, 3315481, 3349255, 3366631, 3369421, 3372211, 3388021, 3405691, 3452191, 3467071, 3477667, 3479887, 3487531, 3503197, 3515431, 3521941, 3523801, 3536821, 3546121, 3571231, 3588445, 3593551, 3608647, 3708871, 3766531, 3766945, 3770515, 3788851, 3796291, 3817681, 3827317, 3885571, 3888361, 3894835, 3901381, 3916261, 3957187, 3999961, 4004101, 4059451, 4126691, 4154161, 4170151, 4205137, 4229601, 4246411, 4330051, 4332511, 4360801, 4363261, 4384171, 4455511, 4524391, 4562521, 4630171, 4724881, 4756861, 4766291, 4806061.

Some larger examples :