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A087321
Smallest multiple of n which is a perfect power (at least a square) of a squarefree number.
7
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
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
KEYWORD
easy,nonn
AUTHOR
Amarnath Murthy, Sep 03 2003
EXTENSIONS
More terms from David Wasserman, May 04 2005
STATUS
approved