%I
%S 1,1,2,3,2,1,5,25,20,16,7,23,39,25,309,455,901,2168,920,1047,
%T 2302,1536,3272,161162,289493,529263,1418949,1562590,579999,
%U 15145,5844471,5244416,65749104,176617384,2077411081,7381004327,10211507191,10333531933,7086785521,8502336136
%N Determinant of the n X n matrix with (i,j)entry equal to 1 or 0 according as i + j is squarefree or not.
%C Conjecture: a(n) is always nonzero. Moreover, a(n)^(1/n) tends to infinity.
%C We have verified that a(n) is nonzero for all n <= 500.
%H ZhiWei Sun, <a href="/A228549/b228549.txt">Table of n, a(n) for n = 1..200</a>
%e a(1) = 1 since 1 + 1 = 2 is squarefree.
%t a[n_]:=a[n]=Det[Table[If[SquareFreeQ[i+j]==True,1,0],{i,1,n},{j,1,n}]]
%t Table[a[n],{n,1,20}]
%Y Cf. A005117, A228548, A069191, A228552.
%K sign
%O 1,3
%A _ZhiWei Sun_, Aug 25 2013
