%I #16 Sep 06 2020 03:45:39

%S 1,1,1,1,1,2,1,1,3,6,1,2,2,2,3,3,1,2,1,2,2,2,1,2,10,10,30,30,6,12,3,3,

%T 3,6,5,10,10,10,3,6,2,2,2,2,30,60,15,30,42,42,42,42,14,28,2,2,2,4,2,4,

%U 4,4,21,21,7,14,7,14,6,6,1,2,2,2,10,10,70,140,7,14,126,126,6,6,30,60

%N Square root of largest square dividing n-th central binomial coefficient.

%H Amiram Eldar, <a href="/A056056/b056056.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000188(A001405(n)).

%t Table[Sqrt@ Max@ Select[Divisors@ Binomial[n, Floor[n/2]], IntegerQ@ Sqrt@ # &], {n, 0, 86}] (* _Michael De Vlieger_, Jul 04 2016 *)

%t a[n_] := Times @@ (First[#]^Floor[Last[#]/2] & /@ FactorInteger[Binomial[n, Floor[n/2]]]); Array[a, 100] (* _Amiram Eldar_, Sep 06 2020 *)

%o (PARI) a(n) = b = binomial(n, n\2); sqrtint(b/core(b)); \\ _Michel Marcus_, Dec 10 2013

%Y Cf. A001405, A000188, A008833, A007913, A055229, A055231, A056057, A056058, A056059, A056060, A056061.

%K nonn

%O 1,6

%A _Labos Elemer_, Jul 26 2000