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amenable n.  and  Carmichael n.

First numbers that belong to both sets:

561, 1105, 1729, 2465, 2821, 6601, 10585, 15841, 29341, 41041, 46657, 52633, 62745, 63973, 75361, 101101, 115921, 126217, 162401, 172081, 188461, 252601, 278545, 294409, 314821, 334153, 340561, 399001, 410041, 449065, 488881, 512461, 530881, 552721, 656601, 658801, 670033, 748657, 825265, 838201, 852841, 997633, 1033669, 1050985, 1082809, 1193221, 1461241, 1569457, 1615681, 1773289, 1857241, 1909001, 2100901, 2113921, 2433601, 2455921, 2508013, 2531845, 2628073, 2704801, 3057601, 3146221, 3224065, 3581761, 3664585, 3828001, 4335241, 4463641, 4767841, 4903921, 4909177, 5031181, 5049001, 5148001, 5310721, 5444489, 5632705, 5968873, 6049681, 6054985, 6189121, 6313681, 6733693, 6840001, 6868261, 7207201, 7519441, 7995169, 8134561, 8341201, 8355841, 8719309, 8719921, 8830801, 8927101, 9439201, 9494101, 9582145, 9585541, 9613297, 9890881, 10024561, 10402561, 10606681, 10837321, 10877581, 11119105, 11205601, 11921001, 11972017, 12261061, 12262321, 12490201, 12945745, 13187665, 13696033, 13992265, 14469841, 14676481, 15247621, 15403285, 15829633, 15888313, 16046641, 16778881, 17098369, 17236801, 17316001, 17586361, 17812081, 18162001, 18307381, 18900973, 19384289, 19683001, 20964961, 21584305, 22665505, 23382529, 25603201, 26280073, 26474581, 26719701, 26921089, 26932081, 27062101, 27336673, 27402481, 28787185, 29020321, 29111881, 31146661, 31405501, 31692805, 32914441, 33302401, 33596641, 34196401, 34657141, 34901461, 35571601, 35703361, 36121345, 36765901, 37167361, 37280881, 37354465, 37964809, 38151361, 38624041, 38637361, 39353665, 40160737, 40280065, 40430401, 40622401, 40917241, 41298985, 41341321, 41471521, 42490801, 43286881, 43331401, 43584481, 43620409, 44238481, 45318561, 45877861, 45890209, 46483633, 47006785, 48321001, 48628801, 49333201, 50201089, 53245921, 53711113, 54767881, 55462177, 56052361, 58489201, 60112885, 60957361, 62756641, 64774081, 65037817, 65241793, 67371265, 67653433, 67994641, 68154001, 69331969, 70561921, 72108421, 72286501, 74165065, 75151441, 75681541, 75765313, 76595761, 77826001, 78091201, 78120001, 79411201, 79624621, 80282161, 80927821, 81638401, 81926461, 82929001, 83099521, 83966401, 84311569, 84350561, 84417985, 87318001, 88689601, 90698401, 92625121, 93030145, 93614521, 93869665, 94536001, 96895441, 99036001, 99830641, 99861985, 100427041, 101649241, 101957401, 102090781, 104404861, 104569501, 104852881, 105117481, 105309289, 105869401, 106041937, 107714881, 109393201, 109577161, 111291181, 114910489, 115039081, 115542505, 116682721, 118901521, 119327041, 120981601, 121247281, 122785741, 124630273, 127664461, 128697361, 129255841, 129762001, 130032865, 130497361, 132511681, 133205761.

Some larger examples :