A365784 a(n) = A126706(n) divided by its squarefree kernel.

2, 3, 2, 4, 2, 6, 4, 2, 3, 8, 5, 2, 9, 4, 2, 3, 2, 12, 5, 2, 8, 2, 4, 3, 2, 16, 7, 3, 10, 4, 18, 8, 2, 3, 4, 2, 3, 2, 9, 4, 2, 24, 7, 2, 5, 4, 3, 2, 16, 27, 2, 4, 3, 2, 5, 8, 6, 4, 2, 9, 32, 14, 3, 20, 2, 3, 8, 2, 36, 2, 16, 15, 2, 4, 3, 2, 8, 11, 2, 7, 4, 25

Offset: 1

Author

Michael De Vlieger, Sep 19 2023

Keywords

• nonn

Comments

Let b(n) = A126706(n) and let squarefree kernel rad(n) = A007947(n).

a(n) > 1, rad(a(n)) | rad(b(n)).

Examples

			a(1) = 2 since b(1)/rad(b(1)) = 12/6 = 2.
a(2) = 3 since b(2)/rad(b(2)) = 18/6 = 3.
a(3) = 2 since b(3)/rad(b(3)) = 20/10 = 2.
a(4) = 4 since b(4)/rad(b(4)) = 24/6 = 4.
a(5) = 2 since b(5)/rad(b(5)) = 28/14 = 2.
a(6) = 6 since b(6)/rad(b(6)) = 36/6 = 6, etc.
		

Links

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

Crossrefs

Cf. A007947, A120944, A126706, A365783.

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..300])) \\ Michel Marcus, Sep 19 2023

Formula

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