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Carmichael n.  and  interprime n.

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First numbers that belong to both sets:

15841, 126217, 656601, 1193221, 2704801, 6189121, 8134561, 8719921, 11205601, 13992265, 40917241, 41298985, 43286881, 56052361, 76595761, 88689601.