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

1,3

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.

Links

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

Example

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

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 *)

Crossrefs

Cf. A005117, A119493.

Sequence in context: A292409 A345989 A333458 * A316490 A102982 A231741

Adjacent sequences: A119511 A119512 A119513 * A119515 A119516 A119517

Keyword

easy,sign

Author

Jonathan Vos Post, May 27 2006

Extensions

More terms from Amiram Eldar, Aug 23 2019

Status

approved