A087321 Smallest multiple of n which is a perfect power (at least a square) of a squarefree number.

1, 4, 9, 4, 25, 36, 49, 8, 9, 100, 121, 36, 169, 196, 225, 16, 289, 36, 361, 100, 441, 484, 529, 216, 25, 676, 27, 196, 841, 900, 961, 32, 1089, 1156, 1225, 36, 1369, 1444, 1521, 1000, 1681, 1764, 1849, 484, 225, 2116, 2209, 1296, 49, 100, 2601, 676, 2809, 216

Offset: 1

Author

Amarnath Murthy, Sep 03 2003

Keywords

• easy
• nonn

Examples

			a(12) = 3*12 = 36 = 6^2.
a(24) = 9*24 = 216 = 6^3.
		

Links

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

Crossrefs

Cf. A007947, A051903, A072774, A087320.

Programs

Mathematica

a[n_] := (Times @@ First@#)^(Max[Max @@ Last@#, 2]) &@ Transpose @ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Feb 23 2021 *)

Formula

If n = p^a*q^b*r^c... p, q, r are primes and max(a, b, c, ...) = K then a(n) = p^K*q^K*r^K...

a(n) = A007947(n)^max(A051903(n), 2). - David Wasserman, May 04 2005

Extensions

More terms from David Wasserman, May 04 2005