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A329140
Numbers whose prime signature is a periodic word.
14
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
OFFSET
1,1
COMMENTS
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.
EXAMPLE
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)
MATHEMATICA
aperQ[q_]:=Array[RotateRight[q, #1]&, Length[q], 1, UnsameQ];
Select[Range[100], !aperQ[Last/@FactorInteger[#]]&]
CROSSREFS
Complement of A329139.
Periodic compositions are A178472.
Periodic binary words are A152061.
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.
Sequence in context: A362606 A130092 A289619 * A362605 A182853 A212168
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 09 2019
STATUS
approved