A070077 Greatest common divisor of n-th squarefree number and n-th cubefree number.

1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 2, 1, 2, 1, 3, 1, 1, 1

Offset

1,2

Comments

a(n) is squarefree.

Conjecture: for any squarefree k exists m such that a(m)=k; see A070078.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Cubefree.

Eric Weisstein's World of Mathematics, Squarefree.

Formula

a(n) = GCD(A005117(n), A004709(n)).

Example

a(10) = GCD(A005117(10), A004709(10)) = GCD(14,11) = 1.
a(11) = GCD(A005117(11), A004709(11)) = GCD(15,12) = 3*GCD(5,4) = 3*1 = 3.

Mathematica

With[{max = 150}, e = Max[FactorInteger[#][[;; , 2]]] & /@ Range[max]; sqf = Flatten[Position[e, _?(# < 2 &)]]; cbf = Flatten[Position[e, _?(# < 3 &)]]; GCD[sqf, cbf[[1 ;; Length[sqf]]]]] (* Amiram Eldar, Oct 20 2023 *)

Crossrefs

Cf. A004709, A005117, A070078.

Sequence in context: A321899 A027870 A357526 * A337200 A337201 A327462

Adjacent sequences: A070074 A070075 A070076 * A070078 A070079 A070080

Keyword

nonn

Author

Reinhard Zumkeller, Apr 22 2002

Status

approved