A369516 Numbers k in A126706 such that neither k-1 nor k+1 is in A126706.

12, 18, 20, 24, 28, 36, 40, 48, 50, 52, 54, 56, 60, 63, 68, 72, 80, 84, 88, 90, 92, 96, 104, 108, 112, 120, 124, 126, 132, 140, 144, 150, 156, 160, 162, 164, 168, 180, 184, 192, 196, 198, 200, 204, 212, 216, 220, 228, 232, 234, 236, 240, 242, 248, 250, 252, 264

Offset: 1

Author

Michael De Vlieger, Mar 24 2024

Keywords

• nonn
• easy

Comments

Singletons in A126706.

The smallest odd term is 63.

Terms are even or divisible by 3, or both. Does not include k coprime to 6; k in A369954 are not in this sequence.

Examples

			Define quality Q to signify a number k neither squarefree nor prime power, i.e., k is in A126706. For example, 12 has quality Q but k = 1..11 do not.
The number 12 is in the sequence since it has quality Q, but neither 11 nor 13 do.
The number 44 is not in the sequence since 45 has quality Q.
The number 99 is not in the sequence because both 98 and 100 have quality Q, etc.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A126706, A369276, A369954.

Programs

Mathematica

Select[Select[Range[264], Nor[SquareFreeQ[#], PrimePowerQ[#]] &], NoneTrue[{# - 1, # + 1}, Nor[SquareFreeQ[#], PrimePowerQ[#]] &] &]
Mean/@SequencePosition[Table[If[!SquareFreeQ[n]&&!PrimePowerQ[n],1,0],{n,300}],{0,1,0}] (* Harvey P. Dale, Jan 30 2025 *)