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%I #26 Jul 29 2022 09:54:35
%S 1,4,9,4,25,36,49,16,9,100,121,36,169,196,225,16,289,36,361,100,441,
%T 484,529,144,25,676,81,196,841,900,961,64,1089,1156,1225,36,1369,1444,
%U 1521,400,1681,1764,1849,484,225,2116,2209,144,49,100,2601,676,2809
%N Smallest square divisible by n.
%H Vaclav Kotesovec, <a href="/A053143/b053143.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 a(n) = n*A007913(n) = A019554(n)^2 = n^2/A008833(n) = (n/A000188(n))^2.
%F Multiplicative with p^e -> p^(e + e mod 2), p prime. - _Reinhard Zumkeller_, Feb 09 2003
%F Dirichlet g.f.: zeta(2s-2)*zeta(s-2)/zeta(2s-4). - _R. J. Mathar_, Oct 31 2011
%F Sum_{k=1..n} a(k) ~ Pi^2 * n^3 / 45. - _Vaclav Kotesovec_, Feb 08 2019
%F Sum_{n>=1} 1/a(n) = 5/2. - _Amiram Eldar_, Jul 29 2022
%t Table[i = 1; While[Mod[i^2, n] > 0, i++]; i^2, {n, 100}] (* _T. D. Noe_, Oct 30 2011 *)
%t f[p_, e_] := p^(e + Mod[e, 2]); a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* _Amiram Eldar_, Aug 29 2019 *)
%o (PARI) a(n) = n*core(n); /* _Joerg Arndt_, Aug 02 2012 */
%Y Cf. A000188, A007913, A008833, A019554.
%K easy,nonn,mult
%O 1,2
%A _Henry Bottomley_, Feb 28 2000
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