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Friedman numbers
A number which can be nontrivially obtained combining all its digits with the basic operations and concatenation. more

The first 600 Friedman numbers :
25, 121, 125, 126, 127, 128, 153, 216, 289, 343, 347, 625, 688, 736, 1022, 1024, 1206, 1255, 1260, 1285, 1296, 1395, 1435, 1503, 1530, 1792, 1827, 2048, 2187, 2349, 2500, 2501, 2502, 2503, 2504, 2505, 2506, 2507, 2508, 2509, 2592, 2737, 2916, 3125, 3159, 3281, 3375, 3378, 3685, 3784, 3864, 3972, 4088, 4096, 4106, 4167, 4536, 4624, 4628, 5120, 5776, 5832, 6144, 6145, 6455, 6880, 7928, 8092, 8192, 9025, 9216, 9261, 10192, 10201, 10251, 10255, 10368, 10426, 10521, 10525, 10575, 10824, 10935, 11025, 11163, 11259, 11264, 11439, 11663, 11664, 11665, 11844, 11848, 11943, 12006, 12060, 12091, 12100, 12101, 12102, 12103, 12104, 12105, 12106, 12107, 12108, 12109, 12167, 12288, 12321, 12337, 12384, 12493, 12505, 12544, 12546, 12550, 12595, 12600, 12762, 12768, 12769, 12798, 12802, 12843, 12850, 12955, 12960, 12964, 12996, 13125, 13176, 13225, 13243, 13286, 13496, 13545, 13689, 13725, 13764, 13813, 13822, 13823, 13824, 13825, 13826, 13832, 13842, 13950, 14035, 14129, 14168, 14175, 14256, 14350, 14352, 14641, 14645, 14647, 15003, 15030, 15125, 15246, 15300, 15345, 15378, 15379, 15435, 15495, 15552, 15562, 15567, 15568, 15585, 15586, 15612, 15613, 15615, 15617, 15618, 15620, 15621, 15622, 15623, 15624, 15625, 15626, 15627, 15628, 15629, 15631, 15632, 15633, 15634, 15635, 15641, 15642, 15645, 15655, 15656, 15661, 15662, 15667, 15679, 15688, 15689, 15697, 15698, 15795, 15975, 16225, 16245, 16272, 16295, 16347, 16348, 16368, 16372, 16374, 16375, 16377, 16378, 16381, 16382, 16384, 16385, 16387, 16447, 16448, 16479, 16743, 16758, 16759, 16765, 16783, 16794, 16797, 16798, 16807, 16815, 16875, 16879, 17253, 17325, 17328, 17346, 17368, 17384, 17428, 17437, 17482, 17488, 17536, 17689, 17856, 17892, 17920, 17925, 18225, 18265, 18270, 18432, 18435, 18522, 18594, 18723, 18744, 19026, 19215, 19321, 19392, 19453, 19592, 19629, 19642, 19653, 19682, 19683, 19684, 19692, 19693, 19732, 19734, 19736, 19737, 19738, 19739, 19773, 19845, 20485, 20736, 21175, 21375, 21495, 21504, 21586, 21606, 21753, 21843, 21844, 21845, 21848, 21870, 21875, 21943, 21952, 21953, 22264, 22528, 22757, 23326, 23328, 23392, 23456, 23490, 23546, 23548, 23552, 23796, 24336, 24339, 24367, 24375, 24385, 24389, 24390, 24393, 24546, 24564, 24566, 24576, 24584, 24586, 24768, 24964, 24972, 25105, 25137, 25314, 25375, 25474, 25510, 25725, 25872, 25895, 25921, 26238, 26244, 26348, 26364, 26496, 26624, 26754, 26896, 26973, 27436, 27634, 27639, 27648, 27653, 27654, 27783, 27889, 28217, 28224, 28226, 28322, 28476, 28547, 28554, 28556, 28559, 28561, 28564, 28671, 28672, 28674, 28678, 28728, 28749, 28764, 28784, 28900, 29160, 29184, 29282, 29517, 29519, 29523, 29524, 29525, 29526, 29527, 29529, 29531, 29549, 29584, 29632, 29768, 29795, 29929, 30625, 31250, 31252, 31256, 31346, 31347, 31509, 31590, 31682, 32685, 32697, 32744, 32747, 32751, 32759, 32761, 32762, 32764, 32765, 32768, 32771, 32772, 32775, 32778, 32781, 32782, 32783, 32785, 32786, 32795, 32805, 32815, 32825, 32832, 32835, 32836, 32845, 32849, 32851, 32853, 32854, 32855, 32859, 32865, 32875, 32885, 32895, 33495, 33579, 33655, 33696, 34425, 34968, 34986, 34991, 34992, 34993, 34996, 35152, 35684, 35721, 35726, 35782, 35928, 35932, 35933, 35937, 35942, 36457, 36549, 36850, 36855, 36864, 36918, 37179, 37187, 37249, 37449, 37668, 37814, 37840, 37845, 37875, 38416, 38424, 38427, 38637, 38640, 38856, 38912, 39216, 39283, 39288, 39294, 39295, 39304, 39313, 39314, 39328, 39342, 39343, 39356, 39358, 39362, 39363, 39366, 39368, 39369, 39372, 39382, 39424, 39456, 39784, 39864, 39945, 41323, 41468, 41472, 41665, 42025, 42336, 42875, 42898, 43264, 43268, 43375, 43688, 43689, 43691, 43692, 43775, 43932, 44375, 44676, 44977, 45056, 45360, 45361, 45362, 45363, 45364, 45365, 45366, 45367, 45368, 45369, 45632, 45684, 45760, 45864, 45873, 45927, 45947, 45957, 45978, 46256, 46368, 46556, 46593, 46608, 46613, 46615, 46619, 46624, 46626, 46630, 46632, 46633, 46635, 46637, 46640, 46641, 46642, 46643, 46644, 46645, 46646, 46647, 46648, 46649, 46650, 46651, 46652, 46653, 46655, 46656, 46657, 46658, 46660, 46661, 46662, 46663, 46664, 46665, 46668, 46672, 46673, 46677, 46684.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 9812 values, from 25 to 999964).

n\r 0  1 
252104602 2 
3412131662525 3 
43254233219562270 4 
519871784192220742045 5 
6228115361299184016301226 6 
71906140913971282128212271309 7 
8215013209641055110410129921215 8 
92149101688010021196777970954868 9 
1060856610518901149137912188711184896 10 
11987903868877881895888886848924855

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.