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A329138
Numbers whose prime signature is a necklace.
16
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
OFFSET
1,1
COMMENTS
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.
EXAMPLE
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)
MATHEMATICA
neckQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And];
Select[Range[2, 100], neckQ[Last/@FactorInteger[#]]&]
CROSSREFS
Complement of A329142.
Binary necklaces are A000031.
Necklace compositions are A008965.
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.
Sequence in context: A053460 A304678 A316529 * A334969 A362619 A065200
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 09 2019
STATUS
approved