A376553 - OEIS

%I #9 Sep 28 2024 07:37:42

%S 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 144,9,9,1,4,25,100,100,25,9,36,4,1,4,1,25,400,225,900,1764,441,196,

%U 49,49,784,4,1,1,16,1,16,16,1,441,441,49,196,49,196,36,9

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

%H Amiram Eldar, <a href="/A376553/b376553.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A350388(A001405(n)).

%F a(n) = A376554(n)^2.

%t 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 (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 Cf. A001405, A350388, A376554, A376555, A376556.

%K nonn

%O 0,7

%A _Amiram Eldar_, Sep 28 2024