cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A119514 #12 Jul 09 2022 12:47:50
%S A119514 1,-1,-4,-84,64,320,1540,-4296,22774,-11504,-5472,13752,-18325,
%T A119514 -4808916,22766346,5005440,519618712,-216839949,-913585532,4352326994,
%U A119514 15724880927,0,-44298224496,783852776697,-173267864064,-601092343023697,26866456767483,39073758546015
%N A119514 Determinant of n X n matrix of first n^2 squarefree numbers.
%C A119514 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.
%H A119514 Amiram Eldar, <a href="/A119514/b119514.txt">Table of n, a(n) for n = 1..898</a>
%e A119514 a(2) = -1 =
%e A119514 |1 2|
%e A119514 |3 5|.
%e A119514 a(3) = -4 =
%e A119514 |.1..2..3|
%e A119514 |.5..6..7|
%e A119514 |10.11.13|.
%t A119514 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 *)
%t A119514 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 *)
%Y A119514 Cf. A005117, A119493.
%K A119514 easy,sign
%O A119514 1,3
%A A119514 _Jonathan Vos Post_, May 27 2006
%E A119514 More terms from _Amiram Eldar_, Aug 23 2019