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%I #20 Sep 08 2022 08:44:57
%S 1,2,3,6,10,10,35,70,42,42,462,462,858,858,2145,4290,24310,24310,
%T 92378,92378,176358,176358,1352078,1352078,520030,520030,222870,
%U 222870,6463230,6463230,100180065,200360130,129644790,129644790,907513530
%N Largest squarefree number dividing n-th central binomial coefficient C(n,[ n/2 ]).
%C a(2k+1)=a(2k+2) unless 2k+1 is in A000225, in which case a(2k+2)=2*a(2k+1). - _Robert Israel_, Jan 21 2020
%H Robert Israel, <a href="/A048633/b048633.txt">Table of n, a(n) for n = 1..3364</a>
%e n=10: C(10,5)=252=2*2*3*3*7. The largest squarefree number dividing the 10th central binomial coefficient is 2*3*7=42. Thus a(10)=42
%p f:= n -> convert(numtheory:-factorset(binomial(n,floor(n/2))),`*`):
%p map(f, [$1..50]); # _Robert Israel_, Jan 21 2020
%t Table[Last@ Select[Divisors@ Binomial[n, Floor[n/2]], SquareFreeQ], {n, 35}] (* _Michael De Vlieger_, Feb 05 2017 *)
%o (PARI) a(n)=factorback(factor(binomial(n,n\2))[,1]) \\ _Charles R Greathouse IV_, Nov 05 2017
%o (Magma) [&*PrimeDivisors(Binomial(n, Floor(n/2))): n in [1..35]]; // _Marius A. Burtea_, Jan 21 2020
%Y Equals A007947(A001405(n)). Cf. A034973, A000225.
%Y See A056058 for another version.
%K nonn
%O 1,2
%A _Labos Elemer_
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