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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.
5
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
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).
MATHEMATICA
aQ[n_] := Length[v = Values @ Counts @ FactorInteger[n][[;; , 2]]] > 1 && Length @ Union @ v == 1; Select[Range[250], aQ] (* Amiram Eldar, Aug 08 2019 *)
CROSSREFS
Numbers n such that A182850(n) = 4. See also A182853, A182855.
Subsequence of A059404 and A182852.
Sequence in context: A332785 A367589 A177425 * A348097 A345381 A328930
KEYWORD
nonn
AUTHOR
Matthew Vandermast, Jan 04 2011
STATUS
approved