This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A342973 #19 Jan 26 2022 08:24:28
%S A342973 12,18,20,24,28,36,40,44,45,48,50,52,54,56,60,63,64,68,75,76,80,81,84,
%T A342973 88,90,92,96,98,99,100,104,112,116,117,120,124,126,132,135,136,140,
%U A342973 144,147,148,150,152,153,156,160,162,164,168,171,172,175,176,180,184,188,189,192
%N A342973 Let f = A008477; nonsquarefree numbers m such that f(m) <> m or f(f(m)) <> m.
%C A342973 Equivalently, with f = A008477, terms m of this sequence are precisely the nonsquarefree numbers for which the iterated sequence {m, f(m), f(f(m)), f(f(f(m))), ... } is not periodic.
%C A342973 The first sixteen terms are the same as A126706, then a(17) = 64 while A126706(17) = 68.
%C A342973 There exist only these 4 possibilities:
%C A342973 -> for every squarefree number m in A005117, f(m) = 1, and iterated sequence is for example: (3, 1, 1, 1, 1, ...).
%C A342973 -> For m nonsquarefree fixed point of f in A008478, f(m) = m, iterated sequence has period = 1, as for example: (4, 4, 4, 4, 4, ...).
%C A342973 -> For m nonsquarefree in A062307, f(m) = q and f(q) = m, iterated sequence has period = 2, as for example: (8, 9, 8, 9, 8, 9, ...).
%C A342973 -> For m in this sequence, f(m) = k and m, k belong to an infinite iterated sequence, as for example: (..., 196, 512, 81, 64, ...) (see example).
%e A342973 196 = 2^2*7^2 => A008477(196) = 2^2*2^7 = 2^9 = 512.
%e A342973 512 = 2^9 => A008477(512) = 9^2 = 81.
%e A342973 81 = 9^2 = 3^4 => A008477(81) = 4^3 = 64.
%e A342973 196, 512, 81, 64 are not terms of (A008478 U A062307), so they belong to this sequence.
%t A342973 fun[p_, e_] := e^p; f[n_] := Times @@ fun @@@ FactorInteger[n]; Select[Range[200], !SquareFreeQ[#] && f[#] != # && f[f[#]] != # &] (* _Amiram Eldar_, Apr 01 2021 *)
%o A342973 (PARI) f(n) = factorback(factor(n)*[0, 1; 1, 0]); \\ A008477
%o A342973 isok(m) = if (!issquarefree(m), my(mm=f(m)); (mm != m) && (f(mm) != m)); \\ _Michel Marcus_, Apr 02 2021
%Y A342973 Equals A013929 \ {A008478 U A062307}.
%Y A342973 Cf. A008477, A342551.
%K A342973 nonn
%O A342973 1,1
%A A342973 _Bernard Schott_, Apr 01 2021