

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. AdamsWatters, 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



