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hyperperfect n.  and  odious n.

First numbers that belong to both sets:

21, 28, 301, 496, 2041, 2133, 3901, 8128, 10693, 16513, 19521, 24601, 26977, 51301, 96361, 130153, 159841, 163201, 306181, 542413, 1063141, 1232053, 1284121, 1403221, 1787917, 1950625, 2462881, 2488201, 2708413, 2884501, 2924101, 3420301, 4013833, 4312681, 4658449, 6392257, 7152001, 7478041, 8766061, 9398593, 9699181, 10445221, 12064333, 13646989, 14444041, 14489437, 15042553, 15407173, 16260901, 16641241, 16904101, 20103001, 23548753, 26249473, 26585233, 28005301, 28449901, 28600321, 29757601, 31696501, 31837801, 32545741, 33550336, 35315221, 35492533, 36171853, 38159521, 38749153, 39147301, 41354041, 41881201, 46596457, 47014801, 48373597, 50809261, 54296677, 55262737, 59675773, 62722153, 62804941, 64220161, 65618101, 79001833, 79089541, 81329701, 88347781, 94472041, 95235601, 95295817, 105070201, 106875541, 108240841, 112803841, 116128021, 118535929, 124035913, 125438101, 127802533, 128990941, 133815229, 134281141, 134959501, 138167929, 140520901, 151547761, 153346261, 155367733, 158813737, 160123261, 162157789, 163331269, 176344741, 181728817, 186898501, 190986001, 191847181, 192317941, 196581361, 204349393, 205100017, 214696441, 228695497, 234784201, 243328381, 244930669, 247005973, 247941649, 258051649, 275797861, 291235093, 291461701, 333080509, 346548133, 350992501, 357858001, 359269021, 362320489, 375014317, 383712781, 407721793, 419745517, 434307901, 438281281, 448644961, 454166017, 454503817, 476610241, 512459221, 528793501, 537399589, 540811477, 542935873, 551522161, 569450701, 573685201, 611417641, 623276617, 639596281, 668541001, 688773781, 690653329, 737640901, 744908701, 749797501, 761997661, 762484417, 775316593, 796622401, 801416221, 808275241, 822000961, 824815681, 848374801, 852687061, 853613713, 867716581, 877148941, 893748277, 914054329, 924642337, 940209541, 969890533, 972261181, 974380921.