A228549 - OEIS

%I #18 Apr 02 2023 09:49:36

%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 Zhi-Wei 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}]

%t Table[With[{nn=x},Det[Table[If[SquareFreeQ[i+j],1,0],{i,nn},{j,nn}]]],{x,40}] (* _Harvey P. Dale_, Apr 02 2023 *)

%Y Cf. A005117, A228548, A069191, A228552.

%K sign

%O 1,3

%A _Zhi-Wei Sun_, Aug 25 2013