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Maximum determinant of an n X n matrix with entries 1, 1/2, .., 1/n^2; numerator.
3

%I #8 Mar 23 2018 20:52:33

%S 1,5,2027,12976897,450724396028209,13238878814817907394909,

%T 280849389948155488261365087763753,

%U 132758211671968916518163154756197108235468015014261

%N Maximum determinant of an n X n matrix with entries 1, 1/2, .., 1/n^2; numerator.

%C The maximum determinant achievable by arranging the fractions 1/1, 1/2, 1/3, ..., 1/n^2 as matrix entries is provided as fraction a(n) / A301533(n).

%H Hugo Pfoertner, <a href="/A301532/a301532.pdf">Illustration of maximum determinant value A301532/A301533</a>.

%e a(3) = 2027, because no matrix with a greater determinant can be found than

%e (1/1 1/7 1/5)

%e (1/4 1/2 1/9)

%e (1/8 1/6 1/3),

%e which has the determinant 2027/15120. A301533(3) = 15120.

%Y Cf. A085000, A301371, A301533 (corresponding denominators)

%K nonn,frac,more

%O 1,2

%A _Hugo Pfoertner_, Mar 23 2018