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A365789 Position of A365787(n) in A024619.

%I A365789 #7 Sep 20 2023 11:53:12
%S A365789 1,3,2,6,10,4,7,17,5,25,29,12,20,42,8,9,26,61,69,23,11,31,48,96,13,22,
%T A365789 111,64,14,44,134,15,16,154,36,28,62,18,19,72,109,210,21,34,54,240,
%U A365789 139,89,24,288,39,181,329,27,55,66,137,45,374,30,99,161,236,32
%N A365789 Position of A365787(n) in A024619.
%C A365789 A365787(n) = A286708(n)/A007947(A286708(n)).
%C A365789 Permutation of natural numbers.
%H A365789 Michael De Vlieger, <a href="/A365789/b365789.txt">Table of n, a(n) for n = 1..4742</a>
%H A365789 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A365789 Let b(n) = A286708(n), rad(n) = A007947(n), and c(n) = A024619(n).
%e A365789 a(1) = 1 since b(1)/rad(b(1)) = 36/6 = 6 = c(1).
%e A365789 a(2) = 3 since b(2)/rad(b(2)) = 72/6 = 12 = c(3).
%e A365789 a(3) = 2 since b(3)/rad(b(3)) = 100/10 = 10 = c(2).
%e A365789 a(4) = 6 since b(4)/rad(b(4)) = 108/6 = 18 = c(6).
%e A365789 a(5) = 10 since b(5)/rad(b(5)) = 144/6 = 24 = c(10).
%e A365789 a(6) = 4 since b(6)/rad(b(6)) = 196/14 = 14 = c(4), etc.
%t A365789 nn = 3600;
%t A365789 s = Rest@
%t A365789   Select[Union@ Flatten@
%t A365789    Table[a^2*b^3, {b, nn^(1/3)}, {a, Sqrt[nn/b^3]}],
%t A365789    Not @* PrimePowerQ];
%t A365789 t = Select[Range[2, nn], Not @* PrimePowerQ];
%t A365789 Map[FirstPosition[t, #/(Times @@ FactorInteger[#][[All, 1]])][[1]] &, s]
%Y A365789 Cf. A007947, A024619, A120944, A286708, A365786, A365787.
%K A365789 nonn
%O A365789 1,2
%A A365789 _Michael De Vlieger_, Sep 19 2023