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

1,2

Comments

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.

Links

Table of n, a(n) for n=1..13.

Al Zimmermann's Programming Contests, Delacorte Numbers, Description, October 2014.

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

Example

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)).

Crossrefs

Cf. A261176, A003989, A018782.

Sequence in context: A200060 A240561 A057122 * A367986 A113119 A067416

Adjacent sequences: A261174 A261175 A261176 * A261178 A261179 A261180

Keyword

nonn,hard

Author

Hugo Pfoertner, Aug 15 2015

Extensions

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

Status

approved