A089384 Greatest squarefree proper divisor of n, a(1) = 1.

1, 1, 1, 2, 1, 3, 1, 2, 3, 5, 1, 6, 1, 7, 5, 2, 1, 6, 1, 10, 7, 11, 1, 6, 5, 13, 3, 14, 1, 15, 1, 2, 11, 17, 7, 6, 1, 19, 13, 10, 1, 21, 1, 22, 15, 23, 1, 6, 7, 10, 17, 26, 1, 6, 11, 14, 19, 29, 1, 30, 1, 31, 21, 2, 13, 33, 1, 34, 23, 35, 1, 6, 1, 37, 15, 38, 11, 39, 1, 10, 3, 41, 1, 42

Offset: 1

Author

Reinhard Zumkeller, Dec 28 2003

Keywords

• nonn

Links

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

Crossrefs

Cf. A005117, A007947, A008966, A013929, A032742.

Programs

Mathematica

a[n_] := If[Max[(f = FactorInteger[n])[[;; , 2]]] == 1, n/f[[1, 1]], Times @@ (First@# & /@ f)]; Array[a, 84] (* Amiram Eldar, Aug 31 2019 *)
Join[{1},Table[Max[Select[Most[Divisors[n]],SquareFreeQ]],{n,2,90}]] (* Harvey P. Dale, Sep 15 2024 *)

Formula

a(n) = if n is squarefree then A032742(n) else A007947(n);

a(n) = A008966(n)*A032742(n) + (1-A008966(n))*A007947(n).