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A329138
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Numbers whose prime signature is a necklace.
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16
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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, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 46, 47, 49, 50, 51, 53, 54, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 75, 77, 78, 79, 81, 82, 83
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refs;
listen;
history;
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internal format)
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OFFSET
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1,1
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COMMENTS
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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.
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:
2: (1)
3: (1)
4: (2)
5: (1)
6: (1,1)
7: (1)
8: (3)
9: (2)
10: (1,1)
11: (1)
13: (1)
14: (1,1)
15: (1,1)
16: (4)
17: (1)
18: (1,2)
19: (1)
21: (1,1)
22: (1,1)
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MATHEMATICA
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neckQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And];
Select[Range[2, 100], neckQ[Last/@FactorInteger[#]]&]
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CROSSREFS
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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 aperiodic are A329139.
Cf. A001037, A025487, A056239, A097318, A112798, A118914, A124010, A181819, A304678, A328596, A329140.
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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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