A057980 - OEIS

A057980

Let n be a positive integer, n>3. Define a tournament on the vertex set {2,3,..,n} by: for i < j, i is adjacent to j if i divides j, else j is adjacent to i. If T(n) denotes its adjacency matrix, then the above sequence is det(T(n))for n=4,5,6....42.

%I #1 May 16 2003 03:00:00

%S 1,0,2,0,2,-6,14,0,44,0,18,-214,308,0,168,0,516,-2008,2328,0,14232,

%T -11124,15552,-29556,95592,0,244464,0,250344,-1012558,1292240,

%U -5809920,11906420,0,-5994822,-7669356,64935420,0,40213980

%N Let n be a positive integer, n>3. Define a tournament on the vertex set {2,3,..,n} by: for i < j, i is adjacent to j if i divides j, else j is adjacent to i. If T(n) denotes its adjacency matrix, then the above sequence is det(T(n))for n=4,5,6....42.

%C MATLAB program was used to generate the tournament matrices T(n) and evaluate determinants. Obviously det(T(n))=0 if n is prime.

%K sign

%O 4,3

%A Rohan Hemasinha (rhemasin(AT)uwf.edu), Nov 27 2000