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deficient n.  and  Friedman n.

First numbers that belong to both sets:

25, 121, 125, 127, 128, 153, 289, 343, 347, 625, 688, 1022, 1024, 1255, 1285, 1395, 1435, 1503, 1827, 2048, 2187, 2349, 2501, 2503, 2504, 2505, 2506, 2507, 2509, 2737, 3125, 3159, 3281, 3375, 3685, 4096, 4106, 4167, 4628, 6145, 6455, 7928, 8192, 9025, 9261, 10201, 10251, 10255, 10426, 10521, 10525, 10575, 10935, 11163, 11259, 11439, 11663, 11665, 11848, 11943, 12091, 12101, 12103, 12105, 12106, 12107, 12109, 12167, 12321, 12337, 12493, 12505, 12550, 12595, 12769, 12802, 12843, 12850, 12955, 13125, 13225, 13243, 13286, 13689, 13725, 13813, 13822, 13823, 13825, 13826, 14035, 14129, 14641, 14645, 14647, 15003, 15125, 15345, 15379, 15495, 15562, 15567, 15585, 15586, 15613, 15615, 15617, 15621, 15622, 15623, 15625, 15626, 15627, 15628, 15629, 15631, 15632, 15633, 15634, 15635, 15641, 15645, 15655, 15656, 15661, 15662, 15667, 15679, 15688, 15689, 15697, 15698, 15795, 15975, 16225, 16245, 16295, 16347, 16348, 16372, 16375, 16377, 16378, 16381, 16382, 16384, 16385, 16387, 16447, 16448, 16479, 16743, 16759, 16765, 16783, 16797, 16798, 16807, 16815, 16875, 16879, 17253, 17384, 17428, 17437, 17482, 17488, 17689, 17925, 18225, 18265, 18435, 18723, 19321, 19453, 19592, 19629, 19642, 19653, 19682, 19683, 19693, 19732, 19736, 19737, 19738, 19739, 19773, 20485, 21175, 21375, 21495, 21586, 21753, 21843, 21844, 21845, 21848, 21875, 21943, 21953, 22757, 23326, 23456, 23546, 24339, 24367, 24375, 24385, 24389, 24393, 24566, 24586, 24964, 25105, 25137, 25375, 25474, 25510, 25725, 25895, 25921, 26896, 26973, 27436, 27634, 27639, 27653, 27783, 27889, 28217, 28226, 28322, 28547, 28556, 28559, 28561, 28564, 28671, 28678, 28749, 29282, 29517, 29519, 29523, 29524, 29525, 29527, 29529, 29531, 29549, 29584, 29632, 29768, 29795, 29929, 30625, 31250, 31252, 31256, 31346, 31347, 31509, 31682, 32685, 32697, 32744, 32747, 32751, 32759, 32761, 32762, 32764, 32765, 32768, 32771, 32775, 32781, 32782, 32783.

Some larger examples :