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

1,2

Links

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

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

Example

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

Mathematica

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

Crossrefs

Cf. A007947, A051903, A072774, A087320.

Sequence in context: A078615 A197863 A087320 * A053143 A068238 A280441

Adjacent sequences: A087318 A087319 A087320 * A087322 A087323 A087324

Keyword

easy,nonn

Author

Amarnath Murthy, Sep 03 2003

Extensions

More terms from David Wasserman, May 04 2005

Status

approved