A396968 - OEIS

%I #5 Jun 19 2026 00:53:22

%S 12,18,20,24,28,44,45,50,52,54,56,60,68,75,76,84,88,90,92,99,116,120,

%T 124,126,132,135,140,147,148,150,152,153,156,162,164,168,172,175,180,

%U 184,188,198,204,207,212,220,228,234,236,240,242,244,245,248,250,260,261

%N Numbers that are neither squarefree, powerful, nor in A396324.

%C A332785 without numbers that are also in A396324.

%C Local complement of A396969 with respect to A332785.

%C 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.

%H Michael De Vlieger, <a href="/A396968/b396968.txt">Table of n, a(n) for n = 1..10000</a>

%t rad[x_] := Times @@ FactorInteger[x][[All, 1]];

%t a332785 = Select[Range[270], Nor[SquareFreeQ[#], Divisible[#, rad[#]^2]] &];

%t Complement[a332785, Select[a332785, Function[k, r = rad[k];

%t   s = Select[Range[k], CoprimeQ[#, k] &];

%t   t = Union@ Flatten@ Mod[

%t     TensorProduct @@

%t     Map[(p = #; NestWhileList[Mod[p*#, k] &, 1, UnsameQ, All]) &,

%t       FactorInteger[k][[All, 1]]], k];

%t   Count[Complement[Range[0, k - 1],

%t     Union[s, t]], _?(Divisible[#, r] &)] > 0] ] ]

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

%K nonn

%O 1,1

%A _Michael De Vlieger_, Jun 14 2026