A365789 Position of A365787(n) in A024619.

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, 111, 64, 14, 44, 134, 15, 16, 154, 36, 28, 62, 18, 19, 72, 109, 210, 21, 34, 54, 240, 139, 89, 24, 288, 39, 181, 329, 27, 55, 66, 137, 45, 374, 30, 99, 161, 236, 32

Offset: 1

Author

Michael De Vlieger, Sep 19 2023

Keywords

• nonn

Comments

A365787(n) = A286708(n)/A007947(A286708(n)).

Permutation of natural numbers.

Examples

			Let b(n) = A286708(n), rad(n) = A007947(n), and c(n) = A024619(n).
a(1) = 1 since b(1)/rad(b(1)) = 36/6 = 6 = c(1).
a(2) = 3 since b(2)/rad(b(2)) = 72/6 = 12 = c(3).
a(3) = 2 since b(3)/rad(b(3)) = 100/10 = 10 = c(2).
a(4) = 6 since b(4)/rad(b(4)) = 108/6 = 18 = c(6).
a(5) = 10 since b(5)/rad(b(5)) = 144/6 = 24 = c(10).
a(6) = 4 since b(6)/rad(b(6)) = 196/14 = 14 = c(4), etc.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..4742
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A007947, A024619, A120944, A286708, A365786, A365787.

Programs

Mathematica

nn = 3600;
s = Rest@
  Select[Union@ Flatten@
   Table[a^2*b^3, {b, nn^(1/3)}, {a, Sqrt[nn/b^3]}],
   Not @* PrimePowerQ];
t = Select[Range[2, nn], Not @* PrimePowerQ];
Map[FirstPosition[t, #/(Times @@ FactorInteger[#][[All, 1]])][[1]] &, s]