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A376553 Largest unitary square divisor of binomial(n, floor(n/2)).

%I A376553 #9 Sep 28 2024 07:37:42
%S A376553 1,1,1,1,1,1,4,1,1,9,36,1,4,4,1,9,9,1,4,1,4,4,1,1,4,100,25,100,25,9,
%T A376553 144,9,9,1,4,25,100,100,25,9,36,4,1,4,1,25,400,225,900,1764,441,196,
%U A376553 49,49,784,4,1,1,16,1,16,16,1,441,441,49,196,49,196,36,9
%N A376553 Largest unitary square divisor of binomial(n, floor(n/2)).
%H A376553 Amiram Eldar, <a href="/A376553/b376553.txt">Table of n, a(n) for n = 0..1000</a>
%F A376553 a(n) = A350388(A001405(n)).
%F A376553 a(n) = A376554(n)^2.
%t A376553 f[p_, e_] := If[EvenQ[e], p^e, 1]; a[0] = a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[Binomial[n, Floor[n/2]]]; Array[a, 100, 0]
%o A376553 (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]));}
%Y A376553 Cf. A001405, A350388, A376554, A376555, A376556.
%K A376553 nonn
%O A376553 0,7
%A A376553 _Amiram Eldar_, Sep 28 2024