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

1,3

Links

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

Formula

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

Example

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.

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]

Crossrefs

Cf. A007947, A120944, A126706, A365783.

Sequence in context: A176572 A168017 A293980 * A368759 A240694 A258643

Adjacent sequences: A365782 A365783 A365784 * A365786 A365787 A365788

Keyword

nonn

Author

Michael De Vlieger, Sep 19 2023

Status

approved