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A329140
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Numbers whose prime signature is a periodic word.
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14
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6, 10, 14, 15, 21, 22, 26, 30, 33, 34, 35, 36, 38, 39, 42, 46, 51, 55, 57, 58, 62, 65, 66, 69, 70, 74, 77, 78, 82, 85, 86, 87, 91, 93, 94, 95, 100, 102, 105, 106, 110, 111, 114, 115, 118, 119, 122, 123, 129, 130, 133, 134, 138, 141, 142, 143, 145, 146, 154
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OFFSET
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1,1
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COMMENTS
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First differs from A182853 in having 2100 = 2^2 * 3^1 * 5^2 * 7^1.
A number's prime signature (A124010) is the sequence of positive exponents in its prime factorization.
A sequence is aperiodic if its cyclic rotations are all different.
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LINKS
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EXAMPLE
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The sequence of terms together with their prime signatures begins:
6: (1,1)
10: (1,1)
14: (1,1)
15: (1,1)
21: (1,1)
22: (1,1)
26: (1,1)
30: (1,1,1)
33: (1,1)
34: (1,1)
35: (1,1)
36: (2,2)
38: (1,1)
39: (1,1)
42: (1,1,1)
46: (1,1)
51: (1,1)
55: (1,1)
57: (1,1)
58: (1,1)
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MATHEMATICA
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aperQ[q_]:=Array[RotateRight[q, #1]&, Length[q], 1, UnsameQ];
Select[Range[100], !aperQ[Last/@FactorInteger[#]]&]
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CROSSREFS
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Numbers whose binary expansion is periodic are A121016.
Numbers whose prime signature is a Lyndon word are A329131.
Numbers whose prime signature is a necklace are A329138.
Cf. A025487, A056239, A097318, A112798, A118914, A124010, A181819, A304678, A329132 A329134, A329143, A329144.
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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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