A329142 - OEIS

A329142

Numbers whose prime signature is not a necklace.

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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OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..57.

EXAMPLE

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)

MATHEMATICA

neckQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And];

Select[Range[100], #==1||!neckQ[Last/@FactorInteger[#]]&]

CROSSREFS

Complement of A329138.

Binary necklaces are A000031.

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.

Sequence in context: A136724 A361868 A316597 * A362620 A112769 A360253

Adjacent sequences: A329139 A329140 A329141 * A329143 A329144 A329145

KEYWORD

nonn

AUTHOR

Gus Wiseman, Nov 09 2019

STATUS

approved