A365785 a(n) = k such that A120944(k) is the squarefree kernel of A126706(n).

1, 1, 2, 1, 3, 1, 2, 6, 4, 1, 2, 7, 1, 3, 8, 5, 10, 1, 4, 12, 2, 14, 6, 8, 15, 1, 3, 9, 2, 7, 1, 3, 19, 13, 8, 20, 14, 22, 4, 10, 24, 1, 5, 25, 8, 12, 16, 27, 2, 1, 28, 14, 18, 30, 11, 6, 8, 15, 34, 5, 1, 3, 22, 2, 36, 23, 7, 38, 1, 39, 3, 4, 41, 19, 27, 43, 8

Offset: 1

Author

Michael De Vlieger, Sep 19 2023

Keywords

• nonn

Examples

			Let b(n) = A126706(n), c(n) = A120944(n), and squarefree kernel rad(n) = A007947(n).
a(1) = 1 since c(1) = rad(b(1)) = rad(12) = 6.
a(2) = 1 since c(1) = rad(b(2)) = rad(18) = 6.
a(3) = 2 since c(2) = rad(b(3)) = rad(20) = 10.
a(4) = 1 since c(1) = rad(b(4)) = rad(24) = 6.
a(5) = 3 since c(3) = rad(b(5)) = rad(28) = 14, etc.
		

Links

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

Crossrefs

Cf. A007947, A120944, A126706, A365783.

Programs

Mathematica

nn = 240;
s = Select[Range[12, nn], Nor[PrimePowerQ[#], SquareFreeQ[#]] &];
t = Select[Range[nn/2], And[SquareFreeQ[#], CompositeQ[#]] &];
Map[FirstPosition[t, Times @@ FactorInteger[#][[All, 1]]][[1]] &, s]

Formula

A120944(a(n)) = A007947(A126706(n)) = A365783(n).