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Carmichael n.  and  odious n.

First numbers that belong to both sets:

1729, 2465, 2821, 6601, 10585, 15841, 29341, 41041, 46657, 52633, 62745, 63973, 75361, 126217, 162401, 294409, 399001, 410041, 530881, 552721, 658801, 670033, 748657, 825265, 852841, 997633, 1024651, 1050985, 1082809, 1461241, 1569457, 1615681, 2113921, 2433601, 2508013, 2704801, 3146221, 3224065, 3581761, 4767841, 4903921, 5148001, 5968873, 6733693, 6840001, 6868261, 7207201, 7519441, 7995169, 8134561, 8355841, 8719309, 8719921, 8830801, 8927101, 9439201, 9582145, 9585541, 9890881, 10024561, 10606681, 11119105, 11205601, 12261061, 12490201, 13187665, 13696033, 14469841, 14676481, 14913991, 15403285, 16046641, 16778881, 17098369, 17586361, 17812081, 18162001, 18307381, 18900973, 19683001, 20964961, 23382529, 26280073, 26932081, 27336673, 29111881, 31146661, 31692805, 32914441, 33302401, 35571601, 36765901, 37167361, 37280881, 37964809, 38151361, 38624041, 38637361, 40160737, 40622401, 40917241, 41341321, 43286881, 43331401, 45318561, 45890209, 46483633, 48321001, 48628801, 49333201, 53245921, 53711113, 54767881, 55462177, 56052361, 60957361, 62756641, 65037817, 67653433, 67902031, 68154001, 69331969, 70561921, 75151441, 75681541, 76595761, 77826001, 78091201, 78120001, 80282161, 81926461, 83099521, 84350561, 87318001, 90698401, 93030145, 94536001, 99036001, 101649241, 101957401, 104852881, 105117481, 105309289, 107714881, 111291181, 115039081, 116682721, 120981601, 121247281, 128697361, 129255841, 129762001, 130032865, 133205761, 133800661, 134809921, 134857801, 135556345, 136625941, 139592101, 139952671, 140241361, 150846961, 153927961, 157731841, 158404141, 159492061, 161035057, 163954561, 169570801, 172290241, 175997185, 178482151, 188689501, 189941761, 196358977, 200753281, 206955841, 213835861, 214852609, 216821881, 221884001, 226509361, 227752993, 230630401, 230996949, 231194965, 238244041, 238527745, 241242001, 242641153, 246446929, 258634741, 271481329, 271794601, 273769921, 277241401, 279377281, 280067761, 280761481, 289766701, 289860481, 291848401, 292776121, 296559361, 299736181, 300614161, 301704985, 302751505, 321602401, 328573477, 333065305, 348612265, 357277921, 357380101, 358940737, 362569201, 364590721, 382304161, 393122521, 393513121, 396262945, 399906001, 403043257, 403317421, 413138881, 413631505, 416964241, 429553345, 434330401, 434932961, 438359041, 440707345, 458368201, 461502097, 471441001, 471905281, 473847121, 481239361, 496050841, 503758801, 509033161, 510825601, 511338241, 517937581, 518117041, 527761081, 530443201, 532758241, 540066241, 544101481, 545570641, 548871961, 549117205, 549333121, 549538081, 551672221, 556199281, 561481921, 561777121, 564651361, 568227241, 577240273, 579606301, 580565233, 590754385, 593234929, 595405201, 600892993, 602593441, 606057985, 611397865, 612347905, 612816751, 616463809, 618068881, 620169409, 625060801, 629692801, 633639097.

Some larger examples :