cp's OEIS Frontend

A087320 Smallest perfect power (at least a square) that is a multiple of n.

%I A087320 #29 Jul 09 2022 11:09:16
%S A087320 1,4,9,4,25,36,49,8,9,100,121,36,169,196,225,16,289,36,361,100,441,
%T A087320 484,529,144,25,676,27,196,841,900,961,32,1089,1156,1225,36,1369,1444,
%U A087320 1521,400,1681,1764,1849,484,225,2116,2209,144,49,100,2601,676,2809,216,3025
%N A087320 Smallest perfect power (at least a square) that is a multiple of n.
%C A087320 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
%C A087320 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
%H A087320 Amiram Eldar, <a href="/A087320/b087320.txt">Table of n, a(n) for n = 1..10000</a>
%F A087320 a(n)/n <= A007947(n) (the squarefree kernel of n).
%F A087320 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
%F A087320 From _Amiram Eldar_, Jul 09 2022: (Start)
%F A087320 a(n) = n iff n is in A001597.
%F A087320 a(n) = n * A160400(n). (End)
%e A087320 a(54) = 216 = 6^3. 54 is the least n such that a(n)/n does not divide A007947(n).
%t A087320 a[n_] := n * SelectFirst[Range[n], GCD @@ FactorInteger[n*#][[;; , 2]] > 1 &]; a[1] = 1; Array[a, 100] (* _Amiram Eldar_, Jul 09 2022 *)
%Y A087320 Cf. A001597, A007947, A087321, A160400, A197863.
%K A087320 easy,nonn
%O A087320 1,2
%A A087320 _Amarnath Murthy_, Sep 03 2003
%E A087320 Edited and extended by _David Wasserman_, May 03 2005