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 A055491 Smallest square divisible by n divided by largest square which divides n. 2

%I

%S 1,4,9,1,25,36,49,4,1,100,121,9,169,196,225,1,289,4,361,25,441,484,

%T 529,36,1,676,9,49,841,900,961,4,1089,1156,1225,1,1369,1444,1521,100,

%U 1681,1764,1849,121,25,2116,2209,9,1,4,2601,169,2809,36,3025,196,3249,3364

%N Smallest square divisible by n divided by largest square which divides n.

%H Reinhard Zumkeller, <a href="/A055491/b055491.txt">Table of n, a(n) for n = 1..10000</a>

%H Henry Bottomley, <a href="http://fs.gallup.unm.edu/Bottomley-Sm-Mult-Functions.htm">Some Smarandache-type multiplicative sequences</a>.

%F If n is written as Product(Pj^Ej) then a(n) = Product(Pj^(2*(Ej mod 2))).

%F a(n) = A053143(n)/A008833(n) = A007913(n)^2 = (A019554(n)/A000188(n))^2 = A000290(n)/A008833(n)^2.

%e a(12) = 36/4 = 9.

%t With[{sqs=Range[100]^2},Table[SelectFirst[sqs,Divisible[#,n]&]/ SelectFirst[ Reverse[sqs],Divisible[n,#]&],{n,60}]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Feb 18 2018 *)

%t f[p_, e_] := p^(2 * Mod[e, 2]); a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* _Amiram Eldar_, Sep 07 2020 *)

%o a055491 = (^ 2) . a007913 -- _Reinhard Zumkeller_, Jul 23 2014

%Y Cf. A056551, A056552.

%Y Cf. A000188, A000290, A007913, A008833, A019554, A053143.

%K easy,nonn,mult

%O 1,2

%A _Henry Bottomley_, Jun 28 2000

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Last modified June 22 20:16 EDT 2021. Contains 345388 sequences. (Running on oeis4.)