A078599 Product of squarefree divisors of n.

1, 2, 3, 2, 5, 36, 7, 2, 3, 100, 11, 36, 13, 196, 225, 2, 17, 36, 19, 100, 441, 484, 23, 36, 5, 676, 3, 196, 29, 810000, 31, 2, 1089, 1156, 1225, 36, 37, 1444, 1521, 100, 41, 3111696, 43, 484, 225, 2116, 47, 36, 7, 100, 2601, 676, 53, 36, 3025, 196, 3249, 3364

Offset: 1

Author

Reinhard Zumkeller, Dec 09 2002

Keywords

• nonn

Examples

			Divisors of n = 20: {1,2,4,5,10,20}, 4 = 2^2 and 20 = 5*2^2, therefore a(20) = 1*2*5*10 = 100.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A005117, A006881, A007875, A007947, A007955, A034444.

Programs

Mathematica

Table[Times@@Select[Divisors[n],SquareFreeQ],{n,60}] (* Harvey P. Dale, Jul 03 2019 *)

Formula

a(n) = a(rad(n)), where rad(n) is the squarefree kernel of n.

a(A006881(n)) = A006881(n)^2.

a(A000040(n)) = A000040(n).

a(n) = A007955(A007947(n)). - T. D. Noe, Jul 08 2008

a(n) = A007947(n)^A007875(n). - Amiram Eldar, Sep 10 2020

a(n) = Product_{d|n} d^(mu(d)^2). - Wesley Ivan Hurt, Dec 03 2023