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

1,2

Comments

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

Permutation of natural numbers.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..4742

Index entries for sequences that are permutations of the natural numbers

Example

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.

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]

Crossrefs

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

Sequence in context: A300070 A171632 A245609 * A072765 A210756 A210748

Adjacent sequences: A365786 A365787 A365788 * A365790 A365791 A365792

Keyword

nonn

Author

Michael De Vlieger, Sep 19 2023

Status

approved