A119514 Determinant of n X n matrix of first n^2 squarefree numbers.

1, -1, -4, -84, 64, 320, 1540, -4296, 22774, -11504, -5472, 13752, -18325, -4808916, 22766346, 5005440, 519618712, -216839949, -913585532, 4352326994, 15724880927, 0, -44298224496, 783852776697, -173267864064, -601092343023697, 26866456767483, 39073758546015

Offset: 1

Author

Jonathan Vos Post, May 27 2006

Keywords

• easy
• sign

Comments

The absolute value of a(1) through a(3) and a(5), are squares. None of the absolute values of a(1) through a(8) are themselves squarefree.

Examples

			a(2) = -1 =
|1 2|
|3 5|.
a(3) = -4 =
|.1..2..3|
|.5..6..7|
|10.11.13|.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..898

Crossrefs

Cf. A005117, A119493.

Programs

Mathematica

s = Select[Range[1500], SquareFreeQ]; n = Length[s]; m = Floor[Sqrt[n]]; seq = {}; Do[mat = Partition[s[[1 ;; k^2]], k]; AppendTo[seq, Det[mat]], {k, 1, m}]; seq (* Amiram Eldar, Aug 23 2019 *)
Module[{nn=30,sqfr},sqfr=Select[Range[2 nn^2],SquareFreeQ];Table[Det[ Partition[ Take[ sqfr,n^2],n]],{n,nn}]] (* Harvey P. Dale, Jul 09 2022 *)

Extensions

More terms from Amiram Eldar, Aug 23 2019