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Carmichael n.  and  evil n.

First numbers that belong to both sets:

561, 1105, 8911, 101101, 115921, 172081, 188461, 252601, 278545, 314821, 334153, 340561, 449065, 488881, 512461, 656601, 838201, 1033669, 1152271, 1193221, 1773289, 1857241, 1909001, 2100901, 2455921, 2531845, 2628073, 3057601, 3664585, 3828001, 4335241, 4463641, 4909177, 5031181, 5049001, 5310721, 5444489, 5481451, 5632705, 6049681, 6054985, 6189121, 6313681, 8341201, 9494101, 9613297, 10267951, 10402561, 10837321, 10877581, 11921001, 11972017, 12262321, 12945745, 13992265, 15247621, 15829633, 15888313, 17236801, 17316001, 19384289, 21584305, 22665505, 25603201, 26474581, 26719701, 26921089, 27062101, 27402481, 28787185, 29020321, 31405501, 33596641, 34196401, 34657141, 34901461, 35703361, 36121345, 37354465, 39353665, 40280065, 40430401, 41298985, 41471521, 42490801, 43584481, 43620409, 44238481, 45877861, 47006785, 50201089, 58489201, 60112885, 64377991, 64774081, 65241793, 67371265, 67994641, 72108421, 72286501, 74165065, 75765313, 79411201, 79624621, 80927821, 81638401, 82929001, 83966401, 84311569, 84417985, 88689601, 92625121, 93614521, 93869665, 96895441, 99830641, 99861985, 100427041, 102090781, 104404861, 104569501, 105869401, 106041937, 109393201, 109577161, 114910489, 115542505, 118901521, 119327041, 122785741, 124630273, 127664461, 130497361, 132511681, 133344793, 144218341, 145124785, 146843929, 151530401, 151813201, 153589801, 158864833, 161242705, 161913961, 167979421, 168659569, 169057801, 170947105, 171454321, 171679561, 172430401, 172947529, 173085121, 174352641, 176659201, 178451857, 178837201, 180115489, 181154701, 182356993, 184353001, 186393481, 186782401, 187188001, 188516329, 193708801, 193910977, 194120389, 194675041, 208969201, 212027401, 214850881, 225745345, 228842209, 237597361, 247095361, 250200721, 252141121, 255160621, 256828321, 257495641, 266003101, 270857521, 274569601, 275283401, 278152381, 288120421, 292244833, 295643089, 295826581, 306871201, 311388337, 318266641, 321197185, 325546585, 329769721, 333229141, 334783585, 338740417, 346808881, 354938221, 360067201, 366532321, 366652201, 367804801, 367939585, 368113411, 382536001, 390489121, 392099401, 393716701, 395044651, 395136505, 405739681, 413058601, 417241045, 419520241, 426821473, 440306461, 455106601, 461854261, 462199681, 477726145, 483006889, 484662529, 490099681, 490503601, 492559141, 499310197, 507726901, 516684961, 518706721, 529782121, 533860309, 542497201, 545363281, 547652161, 552894301, 555465601, 556450777, 557160241, 557795161, 558570961, 558977761, 569332177, 573896881, 597717121, 602074585, 602426161, 609865201, 621101185, 625482001, 631071001, 642708001, 652969351, 662086041, 672389641, 683032801, 684106401, 703995733, 705101761, 707926801, 710382401, 711374401, 722923201, 739444021, 743404663, 765245881, 775866001, 776176261, 781347841, 790020001, 804978721, 809702401, 809883361, 822531841, 833608321, 834720601, 836515681, 839275921.

Some larger examples :