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Friedman n.  and  interprime n.

First numbers that belong to both sets:

625, 736, 1827, 2349, 2592, 4096, 10521, 11259, 12060, 12104, 12108, 12544, 12550, 12595, 13545, 13689, 14175, 15495, 15613, 15624, 15635, 15642, 15645, 15655, 16375, 16479, 16875, 17346, 17368, 17437, 18522, 19684, 19692, 21606, 21952, 24385, 25137, 25725, 26364, 27639, 28224, 28554, 28678, 29160, 29529, 29584, 31256, 31347, 32775, 32781, 32786, 32832, 32836, 33579, 34425, 35928, 35942, 36864, 37875, 38856, 39342, 39363, 39369, 39372, 39456, 39945, 44977, 45369, 45684, 45760, 46626, 46641, 46646, 46656, 46684, 47538, 48754, 48759, 54369, 57645, 58973, 59052, 59058, 62504, 63904, 65488, 65841, 67254, 67950, 69975, 74183, 77459, 78165, 81648, 86724, 91854, 95232, 98325, 98415, 102051, 102382, 102528, 102912, 102942, 103684, 103968, 104375, 104925, 104979, 105021, 106929, 108135, 111536, 111630, 114244, 114684, 116725, 116928, 117567, 117574, 117597, 117651, 117665, 117729, 117754, 117768, 119682, 124483, 124542, 124965, 125010, 125023, 125041, 125058, 125078, 125097, 125950, 126027, 126736, 127435, 127450, 127587, 127680, 128455, 128673, 129600, 129642, 130942, 131250, 132495, 132568, 132615, 132654, 132715, 132854, 133956, 134457, 134584, 134673, 134783, 135429, 135432, 136752, 136854, 137628, 137679, 137718, 137774, 137784, 137797, 137815, 138240, 139896, 139968, 141384, 142805, 144768, 145652, 146335, 146412, 146520, 146758, 147384, 147394, 147399, 147469, 148716, 149396, 150300, 150435, 151250, 151263, 151296, 152460, 152608, 153790, 154336, 155850, 156235, 156247, 156255, 156258, 156264, 159375, 161025, 161050, 161056, 162720, 163217, 163844, 165495, 165894, 166668, 169464, 172386, 172547, 172773, 173664, 174762, 174825, 175632, 176925, 177149, 178560, 179275, 179475, 182784, 183624, 184335, 185935, 186516, 186624, 186648, 186684, 186704, 187136, 187230, 189435, 192375, 192717, 193914, 193968, 194481, 194823, 195112, 195315, 196488, 196581, 196662, 196745, 196824, 196845, 197340, 197370, 197432, 197664, 198024, 198450, 199563, 204800, 205419, 206486, 207936, 209854, 209946, 212576, 212868, 213528, 214368, 215784, 215860, 216003, 216030, 216049, 216066, 216081, 216097, 216225, 217854, 218743.

Some larger examples :