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Determinant of n X n matrix of first n^2 terms of Euler totient function phi (A000010).
1

%I #11 Jul 28 2021 16:54:19

%S 1,0,-16,80,-4640,-1696,-47290368,778240,-1252408320,827269120,

%T -1883587535170560,-167527809024,-660985839681085440,

%U -66300178824585216,-1744375183677849600,29157688117836220727296,5544673967679230591621398528,-134078707495836661579776

%N Determinant of n X n matrix of first n^2 terms of Euler totient function phi (A000010).

%H Harvey P. Dale, <a href="/A119508/b119508.txt">Table of n, a(n) for n = 1..250</a>

%e a(2) = 0 because of the singular matrix 0 =

%e |1 1|

%e |2 2|.

%t nmax = 20; Table[Det[Table[EulerPhi[k*(i-1) + j], {i, 1, k}, {j, 1, k}]], {k, 1, nmax}] (* _Vaclav Kotesovec_, Feb 24 2019 *)

%t Table[Det[Partition[EulerPhi[Range[n^2]],n]],{n,20}] (* _Harvey P. Dale_, Jul 28 2021 *)

%Y Cf. A000010, A119493.

%K easy,sign

%O 1,3

%A _Jonathan Vos Post_, May 27 2006

%E More terms from _Vaclav Kotesovec_, Feb 24 2019