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%I #14 Nov 26 2015 08:40:53
%S 0,10,180,1392,6149,21350,57192,137617,298864,593378,1101739,1936342,
%T 3216080
%N Maximum value of (1/2)*Sum_{i=1..n} Sum_{j=1..n} Sum_{k=1..n} Sum_{l=1..n} gcd(b(i,j),b(k,l)) * ((i-k)^2+(j-l)^2) for an n X n matrix b filled with the integers 1 to n^2.
%C Best results found in Al Zimmermann's Programming Contest "Delacorte Numbers". For more information see A261176. All terms beyond a(5) are conjectured based on numerical results. Terms up to a(11) have at least 5 independent verifications. Lower bounds for the next terms are a(14)>=5189492, a(15)>=8110781, a(16)>=12239616, a(17)>=18073562, a(18)>=26055061, a(19)>=36769303, a(20)>=51095165.
%H Al Zimmermann's Programming Contests, <a href="http://azspcs.com/Contest/DelacorteNumbers">Delacorte Numbers</a>, Description, October 2014.
%H Al Zimmermann's Programming Contests, <a href="http://azspcs.com/Contest/DelacorteNumbers/FinalReport">Delacorte Numbers</a>, Final Report, January 2015.
%e a(3)=180, because no arrangement of the matrix elements exists that produces a larger Delacorte Number than e.g. ((2 3 4)(9 1 5)(8 7 6)).
%Y Cf. A261176, A003989, A018782.
%K nonn,hard
%O 1,2
%A _Hugo Pfoertner_, Aug 15 2015
%E Lower bounds for a(18) and a(20) improved by _Hugo Pfoertner_, Nov 22 2015
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