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A376554 Square root of largest unitary square divisor of binomial(n, floor(n/2)).

%I A376554 #8 Sep 28 2024 07:37:21
%S A376554 1,1,1,1,1,1,2,1,1,3,6,1,2,2,1,3,3,1,2,1,2,2,1,1,2,10,5,10,5,3,12,3,3,
%T A376554 1,2,5,10,10,5,3,6,2,1,2,1,5,20,15,30,42,21,14,7,7,28,2,1,1,4,1,4,4,1,
%U A376554 21,21,7,14,7,14,6,3,1,2,2,1,10,5,35,140,7,14
%N A376554 Square root of largest unitary square divisor of binomial(n, floor(n/2)).
%H A376554 Amiram Eldar, <a href="/A376554/b376554.txt">Table of n, a(n) for n = 0..1000</a>
%F A376554 a(n) = A071974(A001405(n)).
%F A376554 a(n) = sqrt(A376553(n)).
%t A376554 f[p_, e_] := If[EvenQ[e], p^(e/2), 1]; a[0] = a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[Binomial[n, Floor[n/2]]]; Array[a, 100, 0]
%o A376554 (PARI) a(n) = {my(f = factor(binomial(n, n\2))); prod(i = 1, #f~, if(f[i, 2]%2, 1, f[i, 1]^(f[i, 2]/2)));}
%Y A376554 Cf. A001405, A071974, A376553, A376555, A376556.
%K A376554 nonn
%O A376554 0,7
%A A376554 _Amiram Eldar_, Sep 28 2024