OFFSET
1,1
COMMENTS
By symmetry (permutation of rows and of columns, and transposition) all terms are divisible by 72.
Presumably most entries are 0 when n is large. The first occurrence of 0 is a(1229).
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
For n=1, one of the matrices is
[ 2 3 5 ]
[ 7 11 13 ]
[ 17 19 23 ]
which has determinant -78. This is divisible by three of the primes forming the matrix's entries, namely 2, 3 and 13, so it contributes 3 to a(n).
MAPLE
f:= proc(n) local M, P, p;
p:= [seq(ithprime(n+i), i=0..8)];
P:= map(t -> [p[1], op(t)], select(t -> t[1] < t[2] and t[3] < t[6] and t[1] < t[3], combinat:-permute(p[2..9])));
M:= map(t -> LinearAlgebra:-Determinant(Matrix(3, 3, t)), P);
72*numboccur(0, [seq(seq(M[i] mod p[j], i=1..5040), j=1..9)])
end proc:
map(f, [$1..50]);
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Nov 23 2020
STATUS
approved