A228549 Determinant of the n X n matrix with (i,j)-entry equal to 1 or 0 according as i + j is squarefree or not.

1, -1, -2, 3, 2, -1, -5, 25, -20, -16, -7, 23, -39, 25, 309, 455, 901, -2168, 920, 1047, 2302, -1536, 3272, 161162, -289493, -529263, 1418949, -1562590, -579999, 15145, 5844471, 5244416, -65749104, 176617384, 2077411081, 7381004327, 10211507191, -10333531933, 7086785521, 8502336136

Offset: 1

Author

Zhi-Wei Sun, Aug 25 2013

Keywords

• sign

Comments

Conjecture: a(n) is always nonzero. Moreover, |a(n)|^(1/n) tends to infinity.

We have verified that a(n) is nonzero for all n <= 500.

Examples

			a(1) = 1 since 1 + 1 = 2 is squarefree.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A005117, A228548, A069191, A228552.

Programs

Mathematica

a[n_]:=a[n]=Det[Table[If[SquareFreeQ[i+j]==True,1,0],{i,1,n},{j,1,n}]]
Table[a[n],{n,1,20}]
Table[With[{nn=x},Det[Table[If[SquareFreeQ[i+j],1,0],{i,nn},{j,nn}]]],{x,40}] (* Harvey P. Dale, Apr 02 2023 *)