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%I A329138 #6 Nov 10 2019 20:29:34
%S A329138 2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,19,21,22,23,25,26,27,29,30,
%T A329138 31,32,33,34,35,36,37,38,39,41,42,43,46,47,49,50,51,53,54,55,57,58,59,
%U A329138 61,62,64,65,66,67,69,70,71,73,74,75,77,78,79,81,82,83
%N A329138 Numbers whose prime signature is a necklace.
%C A329138 First differs from A304678 in having 1350 = 2^1 * 3^3 * 5^2. First differs from A316529 in having 150 = 2^1 * 3^1 * 5^2.
%C A329138 A number's prime signature (A124010) is the sequence of positive exponents in its prime factorization.
%C A329138 A necklace is a finite sequence that is lexicographically minimal among all of its cyclic rotations.
%e A329138 The sequence of terms together with their prime signatures begins:
%e A329138    2: (1)
%e A329138    3: (1)
%e A329138    4: (2)
%e A329138    5: (1)
%e A329138    6: (1,1)
%e A329138    7: (1)
%e A329138    8: (3)
%e A329138    9: (2)
%e A329138   10: (1,1)
%e A329138   11: (1)
%e A329138   13: (1)
%e A329138   14: (1,1)
%e A329138   15: (1,1)
%e A329138   16: (4)
%e A329138   17: (1)
%e A329138   18: (1,2)
%e A329138   19: (1)
%e A329138   21: (1,1)
%e A329138   22: (1,1)
%t A329138 neckQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And];
%t A329138 Select[Range[2,100],neckQ[Last/@FactorInteger[#]]&]
%Y A329138 Complement of A329142.
%Y A329138 Binary necklaces are A000031.
%Y A329138 Necklace compositions are A008965.
%Y A329138 Numbers whose reversed binary expansion is a necklace are A328595.
%Y A329138 Numbers whose prime signature is a Lyndon word are A329131.
%Y A329138 Numbers whose prime signature is aperiodic are A329139.
%Y A329138 Cf. A001037, A025487, A056239, A097318, A112798, A118914, A124010, A181819, A304678, A328596, A329140.
%K A329138 nonn
%O A329138 1,1
%A A329138 _Gus Wiseman_, Nov 09 2019

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