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

1,1

Comments

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

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

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(PARI) apply(x->(x/factorback(factorint(x)[, 1])), select(x->(!issquarefree(x) && !isprimepower(x)), [1..300])) \\ Michel Marcus, Sep 19 2023

Crossrefs

Cf. A007947, A120944, A126706, A365783.

Sequence in context: A372569 A058973 A155520 * A235912 A339749 A277859

Adjacent sequences: A365781 A365782 A365783 * A365785 A365786 A365787

Keyword

nonn

Author

Michael De Vlieger, Sep 19 2023

Status

approved