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emirpimes  and  Harshad n.

First numbers that belong to both sets:

511, 629, 1011, 1101, 1141, 1387, 1417, 1651, 1679, 3097, 4577, 5833, 6443, 7501, 10109, 10213, 10279, 12563, 13117, 14383, 15409, 15623, 17777, 17887, 18653, 20137, 20197, 22249, 22711, 22793, 24449, 24643, 26221, 26933, 31483, 32071, 33007, 33241, 34901, 35513, 37043, 39007, 41059, 45163, 45611, 50293, 51661, 53843, 54301, 54671, 55003, 55403, 55423, 56107, 56321, 56741, 58811, 60881, 60911, 62441, 62669, 66113, 68333, 68933, 70813, 72587, 75197, 76211, 77593, 79267, 85721, 89291, 90101, 94411, 94891, 95449, 96121, 98239, 100633, 100691, 101593, 102271, 104143, 105593, 107407, 108121, 108341, 109117, 109399, 109801, 109957, 111169, 112333, 113459, 113503, 113873, 114287, 114461, 114979, 115529, 116771, 118133, 118841, 121193, 122699, 123029, 123139, 125203, 125533, 128363, 128929, 129487, 130117, 130373, 130847, 131291, 132917, 134083, 134573, 135451, 136201, 137503, 137899, 138973, 140783, 140923, 141001, 143267, 143531, 143579, 143681, 145751, 146053, 147421, 147821, 148277, 148459, 149063, 149843, 151181, 152113, 154597, 157343, 157387, 161849, 163111, 163421, 164033, 164981, 165757, 166451, 168011, 168107, 168547, 169867, 170153, 171767, 172661, 173413, 174131, 175943, 176801, 177509, 177899, 178043, 180941, 182729, 183331, 183773, 184817, 186323, 189751, 190049, 193099, 193169, 193657, 193691, 196447, 197011, 200089, 200221, 201059, 201103, 202469, 202883, 203851, 204119, 206401, 207271, 209507, 209921, 220267, 221011, 221561, 221611, 222319, 225121, 225653, 226067, 226579, 227723, 229927, 240533, 240557, 240971, 243877, 247783, 249101, 249251, 262333, 263701, 263741, 267871, 269123, 282379, 282511, 286607, 287129, 289633, 300013, 300637, 300703, 301733, 303043, 304727, 306109, 308453, 310913, 311219, 311923, 313361, 315211, 315839, 318421, 321061, 321623, 322541, 323209, 323551, 325603, 327577, 329809, 330001, 330391, 331123, 331417, 331637, 332027, 332443, 332599, 333251, 333811, 335521, 335947, 336197, 337699, 339851, 340309, 341207, 341513, 341573, 342121, 342983, 343229, 344413, 345713, 345991, 346123, 346637, 347689, 349201, 350227, 350311, 352223, 352337, 355477, 356593, 359383, 362011, 362321.

Some larger examples :