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A365784 a(n) = A126706(n) divided by its squarefree kernel.

%I A365784 #8 Sep 19 2023 13:54:03
%S A365784 2,3,2,4,2,6,4,2,3,8,5,2,9,4,2,3,2,12,5,2,8,2,4,3,2,16,7,3,10,4,18,8,
%T A365784 2,3,4,2,3,2,9,4,2,24,7,2,5,4,3,2,16,27,2,4,3,2,5,8,6,4,2,9,32,14,3,
%U A365784 20,2,3,8,2,36,2,16,15,2,4,3,2,8,11,2,7,4,25
%N A365784 a(n) = A126706(n) divided by its squarefree kernel.
%C A365784 Let b(n) = A126706(n) and let squarefree kernel rad(n) = A007947(n).
%C A365784 a(n) > 1, rad(a(n)) | rad(b(n)).
%H A365784 Michael De Vlieger, <a href="/A365784/b365784.txt">Table of n, a(n) for n = 1..10000</a>
%F A365784 a(n) = A126706(n)/A365783(n) = A126706(n)/A007947(A126706(n)).
%e A365784 a(1) = 2 since b(1)/rad(b(1)) = 12/6 = 2.
%e A365784 a(2) = 3 since b(2)/rad(b(2)) = 18/6 = 3.
%e A365784 a(3) = 2 since b(3)/rad(b(3)) = 20/10 = 2.
%e A365784 a(4) = 4 since b(4)/rad(b(4)) = 24/6 = 4.
%e A365784 a(5) = 2 since b(5)/rad(b(5)) = 28/14 = 2.
%e A365784 a(6) = 6 since b(6)/rad(b(6)) = 36/6 = 6, etc.
%t A365784 Map[#/(Times @@ FactorInteger[#][[All, 1]]) &, Select[Range[12, 212], Nor[PrimePowerQ[#], SquareFreeQ[#]] &] ]
%o A365784 (PARI) apply(x->(x/factorback(factorint(x)[, 1])), select(x->(!issquarefree(x) && !isprimepower(x)), [1..300])) \\ _Michel Marcus_, Sep 19 2023
%Y A365784 Cf. A007947, A120944, A126706, A365783.
%K A365784 nonn
%O A365784 1,1
%A A365784 _Michael De Vlieger_, Sep 19 2023