A365783 a(n) = squarefree kernel of A126706(n).

6, 6, 10, 6, 14, 6, 10, 22, 15, 6, 10, 26, 6, 14, 30, 21, 34, 6, 15, 38, 10, 42, 22, 30, 46, 6, 14, 33, 10, 26, 6, 14, 58, 39, 30, 62, 42, 66, 15, 34, 70, 6, 21, 74, 30, 38, 51, 78, 10, 6, 82, 42, 57, 86, 35, 22, 30, 46, 94, 21, 6, 14, 66, 10, 102, 69, 26, 106

Offset: 1

Author

Michael De Vlieger, Sep 19 2023

Keywords

• nonn

Comments

Terms are squarefree and composite, i.e., in A120944.

Examples

			Let b(n) = A126706(n) and let squarefree kernel rad(n) = A007947(n).
a(1) = 6 = rad(b(1)) = rad(12).
a(2) = 6 = rad(b(2)) = rad(18).
a(3) = 10 = rad(b(3)) = rad(20), etc.
		

Links

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

Crossrefs

Cf. A007947, A120944, A126706, A365784, A365785.

Programs

Mathematica

Map[Times @@ FactorInteger[#][[All, 1]] &, Select[Range[12, 212], Nor[PrimePowerQ[#], SquareFreeQ[#]] &] ]

PARI

apply(x->(x/factorback(factorint(x)[, 1])), select(x->(!issquarefree(x) && !isprimepower(x)), [1..1000])) \\ Michel Marcus, Sep 19 2023

Formula

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