A365787 a(n) = A286708(n) divided by its squarefree kernel.

6, 12, 10, 18, 24, 14, 20, 36, 15, 48, 54, 28, 40, 72, 21, 22, 50, 96, 108, 45, 26, 56, 80, 144, 30, 44, 162, 100, 33, 75, 192, 34, 35, 216, 63, 52, 98, 38, 39, 112, 160, 288, 42, 60, 88, 324, 200, 135, 46, 384, 68, 250, 432, 51, 90, 104, 196, 76, 486, 55, 147

Offset

1,1

Comments

Permutation of numbers that are not prime powers A024619.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

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

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

Example

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

Mathematica

nn = 5000;
s = Rest@ Select[Union@ Flatten@
  Table[a^2*b^3, {b, nn^(1/3)}, {a, Sqrt[nn/b^3]}],
  Not @* PrimePowerQ];
t = Select[Range[nn/6], And[SquareFreeQ[#], CompositeQ[#]] &];
Map[FirstPosition[t, Times @@ FactorInteger[#][[All, 1]]][[1]] &, s]

Crossrefs

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

Sequence in context: A164378 A124349 A360719 * A315566 A236926 A134383

Adjacent sequences: A365784 A365785 A365786 * A365788 A365789 A365790

Keyword

nonn

Author

Michael De Vlieger, Sep 19 2023

Status

approved