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 A182854 Integers whose prime signature a) contains at least two distinct numbers, and b) contains no number that occurs less often than any other number. 3
 12, 18, 20, 24, 28, 40, 44, 45, 48, 50, 52, 54, 56, 63, 68, 72, 75, 76, 80, 88, 92, 96, 98, 99, 104, 108, 112, 116, 117, 124, 135, 136, 144, 147, 148, 152, 153, 160, 162, 164, 171, 172, 175, 176, 184, 188, 189, 192, 200, 207, 208, 212, 224, 232, 236, 242, 244, 245 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers that require exactly four iterations to reach a fixed point under the x -> A181819(x) map. In each case, 2 is the fixed point that is reached. (1 is the other fixed point of the x -> A181819(x) map.) Cf. A182850. Not the same sequence as A177425, which is a proper subsequence. 1260 is the first nonmember of A177425 that belongs to this sequence; its prime signature is (2,2,1,1). LINKS Eric Weisstein's World of Mathematics, Fixed Point Eric Weisstein's World of Mathematics, Map EXAMPLE The prime signature of 12 (2^2*3^1) is (2,1). Since (2,1) contains at least two distinct numbers, and since each number that appears in (2,1) appears exactly as often as any other number that appears, 12 belongs to this sequence. 12 also requires exactly four iterations under the x -> A181819(x) map to reach a fixed point (namely, 2) .  A181819(12) = 6;  A181819(6) = 4; A181819(4) = 3;  A181819(3) = 2 (and A181819(2) = 2). CROSSREFS Numbers n such that A182850(n) = 4. See also A182853, A182855. Subsequence of A059404 and A182852. Sequence in context: A200511 A059404 A177425 * A173490 A005101 A124626 Adjacent sequences:  A182851 A182852 A182853 * A182855 A182856 A182857 KEYWORD nonn AUTHOR Matthew Vandermast, Jan 04 2011 STATUS approved

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