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de Polignac n.  and  Harshad n.

First numbers that belong to both sets:

1, 2465, 4311, 6021, 10963, 13351, 14383, 15223, 15957, 17887, 20519, 21073, 21541, 21907, 22049, 25691, 26933, 27475, 28269, 31229, 34561, 36613, 39007, 39393, 40027, 40401, 47219, 49693, 51119, 55423, 57971, 59977, 60005, 61237, 61709, 62001, 64533, 65279, 66663, 69103, 69161, 70813, 71575, 71621, 72523, 72699, 74129, 76329, 76477, 78329, 80201, 80595, 83651, 84625, 90101, 91379, 91511, 92345, 93041, 93043, 96411, 96903, 100165, 100251, 100633, 104143, 104875, 105179, 109649, 114429, 117769, 118335, 118825, 118841, 120275, 122981, 123335, 124035, 124507, 125533, 126217, 126697, 126701, 129487, 130117, 131347, 134159, 135749, 136229, 137299, 137411, 138713, 139213, 140969, 141607, 142291, 147933, 150719, 151181, 151183, 154241, 157301, 157761, 158171, 161849, 163139, 163937, 164981, 166833, 168547, 168875, 173413, 188077, 188125, 189847, 190171, 190867, 191983, 195301, 196641, 196823, 199837, 200317, 201059, 202155, 202469, 204953, 205781, 208047, 209323, 210851, 213427, 215137, 215441, 216659, 218275, 219029, 220207, 220267, 220441, 220609, 220999, 221121, 226423, 227107, 228393, 230129, 230185, 232691, 234413, 234761, 236275, 243877, 247181, 250589, 251735, 252477, 253201, 255809, 256743, 256853, 257531, 257779, 257827, 258941, 259777, 264401, 266197, 268337, 269109, 269123, 270297, 271825, 273267, 274079, 274563, 274567, 276161, 277733, 277865, 279757, 280117, 281129, 281143, 284519, 286511, 287651, 289633, 289747, 290651, 295979, 299737, 301663, 305083, 307241, 308039, 308275, 310063, 310221, 310937, 316319, 318627, 319525, 321997, 324185, 324787, 327911, 328325, 331417, 331499, 331749, 333127, 333293, 334153, 335367, 335947, 338067, 339329, 339697, 341513, 341939, 343229, 343467, 344471, 346637, 347665, 348909, 349029, 350001, 350081, 350311, 351509, 355839, 360129, 361171, 361775, 364851, 366637, 368039, 370139, 372209, 376779, 377897, 378081, 381089, 381159, 381625, 382145, 382819, 383377, 384493, 386309, 386831, 387423, 388981, 389647, 394151, 397327, 397413, 402845, 403237, 404263, 405459, 406667, 407189, 410077, 410697, 411539, 412813, 413023, 416585, 416921, 419647, 422603, 422849, 423073, 425615, 426029, 427271, 427547.

Some larger examples :