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

1,2

Links

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

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A361581 A361580 A353975 * A183103 A183105 A316608

Adjacent sequences: A078596 A078597 A078598 * A078600 A078601 A078602

Keyword

nonn

Author

Reinhard Zumkeller, Dec 09 2002

Status

approved