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A087320 Smallest perfect power (at least a square) that is a multiple of n. 5
1, 4, 9, 4, 25, 36, 49, 8, 9, 100, 121, 36, 169, 196, 225, 16, 289, 36, 361, 100, 441, 484, 529, 144, 25, 676, 27, 196, 841, 900, 961, 32, 1089, 1156, 1225, 36, 1369, 1444, 1521, 400, 1681, 1764, 1849, 484, 225, 2116, 2209, 144, 49, 100, 2601, 676, 2809, 216, 3025 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n)/n <= A007947(n) (the squarefree kernel of n).

The prime signature of a(n) is not determined by the prime signature of n. For example, a(2^3*3^5) = 2^3*3^6, but a(2^3*5^5) = 2^5*5^5. - David Wasserman, May 03 2005

Likewise, this sequence is not multiplicative. The smallest exception is a(24) = 144 > 72 = a(3)*a(8). - Franklin T. Adams-Watters, Oct 18 2011

a(p^k) = p^k, a(k) = A007947(k)^2 for cubefree k. Furthermore, the upper bound on a(n)/n can be tightened to A007913(n). - Charlie Neder, Dec 26 2018

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

a(54) = 216 = 6^3. 54 is the least n such that a(n)/n does not divide A007947(n).

CROSSREFS

Cf. A007947, A087321, A197863.

Sequence in context: A345304 A078615 A197863 * A087321 A053143 A068238

Adjacent sequences:  A087317 A087318 A087319 * A087321 A087322 A087323

KEYWORD

easy,nonn

AUTHOR

Amarnath Murthy, Sep 03 2003

EXTENSIONS

Edited and extended by David Wasserman, May 03 2005

STATUS

approved

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Last modified October 20 08:28 EDT 2021. Contains 348099 sequences. (Running on oeis4.)