A365787 - OEIS

%I #7 Sep 20 2023 11:52:57

%S 6,12,10,18,24,14,20,36,15,48,54,28,40,72,21,22,50,96,108,45,26,56,80,

%T 144,30,44,162,100,33,75,192,34,35,216,63,52,98,38,39,112,160,288,42,

%U 60,88,324,200,135,46,384,68,250,432,51,90,104,196,76,486,55,147

%N a(n) = A286708(n) divided by its squarefree kernel.

%C Permutation of numbers that are not prime powers A024619.

%H Michael De Vlieger, <a href="/A365787/b365787.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A286708(n)/A007947(A286708(n)) = A286708(n)/A365786(n).

%F Let b(n) = A286708(n) and let squarefree kernel rad(n) = A007947(n). a(n) >= n such that rad(a(n)) | n.

%e a(1) = 2 since b(1)/rad(b(1)) = 36/6 = 6.

%e a(2) = 3 since b(2)/rad(b(2)) = 72/6 = 12.

%e a(3) = 2 since b(3)/rad(b(3)) = 100/10 = 10.

%e a(4) = 4 since b(4)/rad(b(4)) = 108/6 = 18.

%e a(5) = 2 since b(5)/rad(b(5)) = 144/6 = 24.

%e a(6) = 6 since b(6)/rad(b(6)) = 196/14 = 14, etc

%t nn = 5000;

%t s = Rest@ Select[Union@ Flatten@

%t   Table[a^2*b^3, {b, nn^(1/3)}, {a, Sqrt[nn/b^3]}],

%t   Not @* PrimePowerQ];

%t t = Select[Range[nn/6], And[SquareFreeQ[#], CompositeQ[#]] &];

%t Map[FirstPosition[t, Times @@ FactorInteger[#][[All, 1]]][[1]] &, s]

%Y Cf. A007947, A024619, A120944, A286708, A365786.

%K nonn

%O 1,1

%A _Michael De Vlieger_, Sep 19 2023