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A365785 a(n) = k such that A120944(k) is the squarefree kernel of A126706(n).

%I A365785 #8 Sep 20 2023 11:53:23
%S A365785 1,1,2,1,3,1,2,6,4,1,2,7,1,3,8,5,10,1,4,12,2,14,6,8,15,1,3,9,2,7,1,3,
%T A365785 19,13,8,20,14,22,4,10,24,1,5,25,8,12,16,27,2,1,28,14,18,30,11,6,8,15,
%U A365785 34,5,1,3,22,2,36,23,7,38,1,39,3,4,41,19,27,43,8
%N A365785 a(n) = k such that A120944(k) is the squarefree kernel of A126706(n).
%H A365785 Michael De Vlieger, <a href="/A365785/b365785.txt">Table of n, a(n) for n = 1..10000</a>
%F A365785 A120944(a(n)) = A007947(A126706(n)) = A365783(n).
%e A365785 Let b(n) = A126706(n), c(n) = A120944(n), and squarefree kernel rad(n) = A007947(n).
%e A365785 a(1) = 1 since c(1) = rad(b(1)) = rad(12) = 6.
%e A365785 a(2) = 1 since c(1) = rad(b(2)) = rad(18) = 6.
%e A365785 a(3) = 2 since c(2) = rad(b(3)) = rad(20) = 10.
%e A365785 a(4) = 1 since c(1) = rad(b(4)) = rad(24) = 6.
%e A365785 a(5) = 3 since c(3) = rad(b(5)) = rad(28) = 14, etc.
%t A365785 nn = 240;
%t A365785 s = Select[Range[12, nn], Nor[PrimePowerQ[#], SquareFreeQ[#]] &];
%t A365785 t = Select[Range[nn/2], And[SquareFreeQ[#], CompositeQ[#]] &];
%t A365785 Map[FirstPosition[t, Times @@ FactorInteger[#][[All, 1]]][[1]] &, s]
%Y A365785 Cf. A007947, A120944, A126706, A365783.
%K A365785 nonn
%O A365785 1,3
%A A365785 _Michael De Vlieger_, Sep 19 2023