A396968 Numbers that are neither squarefree, powerful, nor in A396324.

12, 18, 20, 24, 28, 44, 45, 50, 52, 54, 56, 60, 68, 75, 76, 84, 88, 90, 92, 99, 116, 120, 124, 126, 132, 135, 140, 147, 148, 150, 152, 153, 156, 162, 164, 168, 172, 175, 180, 184, 188, 198, 204, 207, 212, 220, 228, 234, 236, 240, 242, 244, 245, 248, 250, 260, 261

Offset

1,1

Comments

A332785 without numbers that are also in A396324.

Local complement of A396969 with respect to A332785.

Superset of A366825, since for k in A366825, k = lpf(k)*rad(k). Therefore, since lpf(k)*rad(k) is the smallest number that exceeds rad(k), then all r < k such that rad(k) | r (i.e., rad(k) itself) also divide k.

Links

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

Mathematica

rad[x_] := Times @@ FactorInteger[x][[All, 1]];
a332785 = Select[Range[270], Nor[SquareFreeQ[#], Divisible[#, rad[#]^2]] &];
Complement[a332785, Select[a332785, Function[k, r = rad[k];
  s = Select[Range[k], CoprimeQ[#, k] &];
  t = Union@ Flatten@ Mod[
    TensorProduct @@
    Map[(p = #; NestWhileList[Mod[p*#, k] &, 1, UnsameQ, All]) &,
      FactorInteger[k][[All, 1]]], k];
  Count[Complement[Range[0, k - 1],
    Union[s, t]], _?(Divisible[#, r] &)] > 0] ] ]

Crossrefs

Cf. A007947, A332785, A366825, A396324, A396968.

Sequence in context: A389227 A364996 A391026 * A363082 A270660 A383488

Adjacent sequences: A396964 A396966 A396967 * A396969 A396970 A396971

Keyword

nonn

Author

Michael De Vlieger, Jun 14 2026

Status

approved