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A329142
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Numbers whose prime signature is not a necklace.
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8
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1, 12, 20, 24, 28, 40, 44, 45, 48, 52, 56, 60, 63, 68, 72, 76, 80, 84, 88, 90, 92, 96, 99, 104, 112, 116, 117, 120, 124, 126, 132, 135, 136, 140, 144, 148, 152, 153, 156, 160, 164, 168, 171, 172, 175, 176, 180, 184, 188, 189, 192, 198, 200, 204, 207, 208, 212
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listen;
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OFFSET
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1,2
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COMMENTS
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After a(1) = 1, first differs from A112769 in lacking 1350.
A number's prime signature (A124010) is the sequence of positive exponents in its prime factorization.
A necklace is a finite sequence that is lexicographically minimal among all of its cyclic rotations.
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LINKS
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EXAMPLE
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The sequence of terms together with their prime signatures begins:
1: ()
12: (2,1)
20: (2,1)
24: (3,1)
28: (2,1)
40: (3,1)
44: (2,1)
45: (2,1)
48: (4,1)
52: (2,1)
56: (3,1)
60: (2,1,1)
63: (2,1)
68: (2,1)
72: (3,2)
76: (2,1)
80: (4,1)
84: (2,1,1)
88: (3,1)
90: (1,2,1)
92: (2,1)
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MATHEMATICA
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neckQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And];
Select[Range[100], #==1||!neckQ[Last/@FactorInteger[#]]&]
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CROSSREFS
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Non-necklace compositions are A329145.
Numbers whose reversed binary expansion is a necklace are A328595.
Numbers whose prime signature is a Lyndon word are A329131.
Numbers whose prime signature is periodic are A329140.
Cf. A001037, A008965, A025487, A056239, A097318, A112798, A118914, A124010, A181819, A304678, A328596, A329139.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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