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Friedman n.  and  inconsummate n.

First numbers that belong to both sets:

216, 2592, 3281, 3864, 3972, 4088, 4106, 4536, 8192, 9261, 10251, 10368, 11025, 12107, 15378, 15626, 15632, 15641, 15642, 15656, 15975, 16375, 17437, 18432, 19592, 19653, 19682, 19737, 25137, 25314, 25872, 28217, 28226, 28322, 28476, 28547, 28554, 28764, 29531, 29549, 31347, 32685, 32697, 32751, 32759, 32762, 32765, 32775, 32781, 32805, 32825, 32832, 32849, 32855, 32859, 32865, 32885, 33696, 34425, 34992, 35937, 36457, 36549, 36855, 36864, 36918, 37179, 37187, 37449, 37668, 37875, 38640, 39342, 39356, 39363, 39372, 42336, 43692, 44676, 45360, 45363, 45632, 45927, 45978, 46556, 46658, 46661, 48672, 48750, 48752, 48753, 48756, 49584, 51398, 51759, 52493, 52947, 56295, 57644, 59048, 59051, 59054, 59055, 59094, 59147, 59265, 59273, 59313, 59319, 59375, 59409, 65478, 65480, 65481, 65484, 65487, 65528, 65841, 67149, 69255, 69822, 69975, 69984, 72576, 74892, 78116, 78126, 78152, 78165, 81920, 82944, 85293, 87381, 91853, 94395, 98325, 98435, 99225, 102392, 102497, 102510, 102528, 102912, 102942, 103680, 103682, 103684, 103685, 103689, 104888, 104925, 104958, 109358, 109473, 110250, 110758, 111536, 114248, 114291, 114377, 114627, 114647, 114681, 114687, 114696, 114737, 114772, 115934, 116342, 116625, 116675, 116745, 116937, 117587, 117627, 117644, 117647, 117648, 117651, 117654, 117657, 117659, 117662, 117665, 117677, 117696, 117697, 117698, 117765, 117767, 118259, 118926, 119375, 119682, 123648, 124362, 124751, 124991, 125021, 125022, 125027, 125031, 125033, 125036, 125037, 125048, 125051, 125054, 125055, 125061, 125066, 125071, 125072, 125081, 125087, 125088, 125091, 125094, 125096, 125097, 125099, 125364, 125648, 125952, 126737, 126753, 127744, 128481, 129438, 129608, 129642, 129888, 130248, 132497, 132498, 132545, 132567, 132587, 132725, 133125, 133815, 135828, 135837, 136214, 136485, 136590, 136754, 136892, 136944, 137625, 137718, 137768, 137769, 137772, 137774, 137837, 138392, 139281, 139392, 139677, 139824, 139896, 139905, 139932, 139962, 139964, 139965, 139967, 140528, 142296, 142805, 142875, 142884, 142892, 143255, 143325, 143357, 143465, 143648, 143739.

Some larger examples :