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Friedman n.  and  unprimeable n.

First numbers that belong to both sets:

625, 1260, 1792, 2048, 3685, 3784, 3972, 4088, 4106, 4536, 5120, 9216, 10575, 10824, 11664, 11665, 11844, 11848, 12060, 12384, 12595, 12996, 13286, 13545, 13950, 14168, 14350, 14352, 14645, 15632, 15634, 15635, 15655, 15656, 15698, 16295, 16372, 16374, 16375, 16378, 16794, 16798, 17368, 17428, 18270, 19026, 19642, 21952, 22264, 22528, 23796, 24385, 24564, 24566, 24584, 24586, 25105, 25314, 25510, 25725, 25895, 26364, 28322, 28564, 28672, 28674, 28678, 28764, 29184, 29795, 30625, 31346, 31590, 32762, 32764, 32765, 32768, 32815, 32825, 32854, 32855, 32875, 32895, 33655, 33696, 34992, 34996, 35684, 35782, 35942, 36864, 38416, 38424, 38640, 39288, 39424, 39784, 39945, 42875, 43375, 43688, 44676, 45684, 46256, 46368, 46624, 46626, 46650, 46652, 46655, 46656, 46658, 49584, 49968, 51398, 52498, 53245, 53248, 53824, 54476, 59032, 59038, 59044, 59045, 59046, 59048, 59314, 59318, 61435, 63895, 63985, 64522, 64868, 65344, 65480, 65482, 65484, 65485, 65486, 65488, 67228, 67252, 67254, 68644, 68800, 69975, 69984, 69985, 73926, 73984, 78115, 78116, 82942, 82944, 82952, 83524, 85264, 85358, 91854, 92160, 93294, 93642, 97336, 98304, 98305, 98435, 100255, 102382, 102384, 102510, 102784, 102942, 103824, 104260, 104375, 104448, 104816, 104888, 104925, 104966, 104968, 105295, 105624, 105625, 107632, 107654, 108612, 109236, 109525, 111132, 112468, 112536, 112590, 112895, 112896, 114242, 114244, 114245, 114246, 114248, 114352, 114390, 114395, 115625, 116318, 116565, 116625, 116640, 116675, 116725, 116778, 117184, 117396, 117466, 117475, 117476, 117584, 117586, 117595, 117596, 117622, 117624, 117625, 117626, 117628, 117630, 117632, 117634, 117635, 117636, 117638, 117660, 117662, 117664, 117665, 117666, 117668, 117684, 117685, 117686, 117694, 117695, 117696, 117698, 117746, 118328, 118336, 118440, 118480, 119375, 119430, 120006, 121815, 123245, 123354, 123538, 123648, 123765, 123768, 123840, 123894, 123896, 123904, 124375, 124385, 124386, 124398, 124412, 124415, 124416, 124464, 124468, 124585, 124684, 124926, 124936, 124964, 124965, 124968, 125030.

Some larger examples :