A261176 -id:A261176 - cp's OEIS frontend

A261177 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.

0, 10, 180, 1392, 6149, 21350, 57192, 137617, 298864, 593378, 1101739, 1936342, 3216080

Offset: 1

Hugo Pfoertner, Aug 15 2015

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.

			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)).

Al Zimmermann's Programming Contests, Delacorte Numbers, Description, October 2014.
Al Zimmermann's Programming Contests, Delacorte Numbers, Final Report, January 2015.

Cf. A261176, A003989, A018782.

Lower bounds for a(18) and a(20) improved by Hugo Pfoertner, Nov 22 2015

cp's OEIS Frontend

A261177 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.

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cp's OEIS Frontend

A261177 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.

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A261177 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.