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amenable n.  and  weakly prime

First numbers that belong to both sets:

294001, 584141, 1282529, 1524181, 2690201, 3085553, 3326489, 5564453, 7204777, 7469789, 7469797, 8090057, 8532761, 8639089, 9608189, 10564877, 14075273, 14151757, 15973733, 16497121, 17424721, 18561293, 18953677, 20414561, 21044557, 21089489, 21496661, 21717601, 22138349, 23462969, 25081361, 25475617, 25556941, 26521721, 27425521, 27469241, 28046353, 28978889, 29348797, 30915637, 30964013, 31240481, 32524313, 33051769, 34349969, 35954509, 36221597, 37448137, 39397009, 39689597, 39724417, 40085977, 40432489, 40812781, 41980441, 42120581, 42145837, 42758917, 43414669, 43432409, 44617561, 45420457, 47263001, 48384977, 49353841, 50030077, 50170513, 50471857, 51340909, 52127189, 53355689, 53454589, 54292081, 55204889, 56485057, 56743469, 57177889, 58020581, 58091653, 58107953, 58572593, 59160317, 59704529, 61089089, 61552901, 62324861, 62444033, 62552489, 62725253, 63359161, 64085921, 64843237, 65029997, 65702393, 65947213, 66640253, 66854549, 67296517, 67715653, 68030449, 68970457, 69505109, 70006253, 70078549, 70514141, 70850641, 71364053, 71370853, 71756029, 71760109, 72168857, 72422393, 72504457, 72673213, 72760297, 73022273, 73179193, 73644101, 74143801, 75374149, 75448801, 75460849, 76456141, 77250497, 77438461, 77444701, 77540017, 78050209, 78712681, 79833133, 81397777, 81434501, 81536501, 81608981, 81811589, 82087813, 82892633, 83880829, 84159917, 85415249, 85478369, 85637089, 86688269, 87303817, 88826693, 89006641, 89473777, 89819413, 90997241, 92027977, 92305589, 92782441, 94113781, 95401417, 95517517, 95532289, 95663761, 97069493, 97165001, 97283321, 97792117, 97864961, 97994641, 98285017, 98451193, 98750609, 98954621, 100447177, 101413777, 102871081, 103291453, 104908273, 110548133, 111033269, 111522709, 111627713, 112663181, 116297257, 117302429, 118121197, 118966829, 119075857, 122047117, 122773549, 126270601, 127311133, 128456557, 128885389, 130859077, 132077149, 134143837, 134528677, 135085453, 135272429, 136240781, 137083109, 137813021, 139452133, 141187097, 142380013, 142790317, 143561773, 143924173, 144481273, 144536701, 146020961, 146610701, 147826829, 147846253, 148421633, 149411569, 154377841, 154467277, 156251789, 156394657, 156693529, 157553993, 159290381, 162066193, 162123869, 162417733, 162524249, 162630497, 163146457, 163482377, 164076173, 164787449, 165862253, 165994513, 167056709, 167637101, 167753561, 169567081, 170448713, 171154673, 172155173, 172535497, 173011789, 173050477, 174465541, 175110097, 175489417, 175988881, 176598493, 178014517, 180044797, 180552809, 181946617, 182363249, 182386921, 183585973, 183838177, 184116337, 184972289, 185627177, 186000169, 186343193, 190056833, 190530629, 193837841, 194846149, 196363373, 197964253, 198303601, 199802621, 201067729, 201674041, 204677017, 206845729, 207091853, 207773861, 208278557, 209297449, 209538169, 211848541, 212040557, 212083709, 215329753, 216553829, 216826097.

Some larger examples :