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

1,1

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.

Links

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

Example

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.

Mathematica

Select[Select[Range[264], Nor[SquareFreeQ[#], PrimePowerQ[#]] &], NoneTrue[{# - 1, # + 1}, Nor[SquareFreeQ[#], PrimePowerQ[#]] &] &]

Crossrefs

Cf. A126706, A369276, A369954.

Sequence in context: A200511 A370409 A363101 * A317711 A359890 A323055

Adjacent sequences: A369513 A369514 A369515 * A369517 A369518 A369519

Keyword

nonn,easy

Author

Michael De Vlieger, Mar 24 2024

Status

approved