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economical n.  and  unprimeable n.

First numbers that belong to both sets:

320, 512, 625, 896, 1072, 1075, 1134, 1135, 1136, 1138, 1142, 1145, 1262, 1264, 1335, 1344, 1345, 1346, 1354, 1355, 1358, 1415, 1418, 1465, 1466, 1502, 1504, 1505, 1642, 1645, 1646, 1675, 1678, 1682, 1685, 1714, 1715, 1718, 1762, 1765, 1766, 1792, 1795, 1855, 1856, 1858, 1894, 1895, 1920, 1922, 1966, 2045, 2048, 2075, 2105, 2195, 2368, 2485, 2495, 2515, 2560, 2944, 3095, 3155, 3235, 3265, 3505, 3665, 3750, 3755, 3785, 4105, 4145, 4195, 4315, 4385, 4415, 4418, 4435, 4535, 4555, 4685, 4765, 4855, 5120, 5125, 5248, 5312, 5375, 5376, 5618, 6400, 6625, 7168, 7375, 7424, 7442, 7776, 7808, 8405, 8875, 9088, 10015, 10016, 10018, 10022, 10025, 10042, 10045, 10046, 10048, 10055, 10082, 10085, 10086, 10125, 10126, 10202, 10206, 10235, 10238, 10290, 10294, 10295, 10375, 10378, 10385, 10402, 10405, 10415, 10418, 10445, 10448, 10544, 10546, 10576, 10645, 10646, 10648, 10675, 10745, 10762, 10765, 10766, 10768, 10805, 10814, 10816, 10822, 10825, 10826, 10874, 10875, 10915, 10928, 10966, 11014, 11015, 11018, 11035, 11038, 11104, 11105, 11122, 11125, 11126, 11182, 11185, 11200, 11205, 11225, 11302, 11306, 11335, 11338, 11344, 11345, 11375, 11378, 11402, 11405, 11455, 11456, 11534, 11535, 11566, 11602, 11606, 11642, 11648, 11662, 11664, 11665, 11722, 11725, 11728, 11750, 11755, 11758, 11762, 11794, 11795, 11840, 11846, 11854, 11855, 11872, 11875, 11878, 11915, 11995, 11998, 12022, 12026, 12055, 12058, 12082, 12085, 12086, 12125, 12128, 12134, 12135, 12175, 12176, 12178, 12182, 12185, 12295, 12315, 12334, 12335, 12352, 12355, 12362, 12365, 12368, 12385, 12442, 12448, 12592, 12598, 12622, 12625, 12775, 12778, 12832, 12864, 12865, 12866, 12875, 12938, 12992, 12994, 12998, 13025, 13055, 13056, 13058, 13075, 13085, 13088, 13114, 13115, 13118, 13135, 13136, 13138, 13198, 13232, 13235, 13238, 13274, 13280, 13285, 13342, 13346, 13355, 13358, 13375.

Some larger examples :