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%I #3 Mar 30 2012 17:27:41
%S 2,1,4,1,16,2,1,1,1,1,9,2,1,1,2,1,4,2,2,3,2,8,17,2,1,8,19,7,1,2,4,1,1,
%T 14,1,1,9,11,4,5,1,6,4,65,15,13,1,1,5,1,1,1,79,11,14,4,13,1,2,1,7,14,
%U 1,20,4,8,1,29,23,4,1,11,26,26,1,1,5,22,5,75,2,1,1,1,3,4,2,43,1,11,11,4,5
%N Greatest common divisor of quadruples a,b,c,d such that a < b < c < d, (a*b*c) mod (a+b+c) = d, (a*b*d) mod (a+b+d) = c, (a*c*d) mod (a+c+d) = b, (b*c*d) mod (b+c+d) = a. The quadruples are ordered according to sum of first three components, secondary by first component, thirdly by second component.
%C First, second, third and fourth component of the quadruples are resp. in A092887, A092888, A092889, A092890.
%e The third quadruple is 12, 60, 128, 160, hence a(3) = gcd(4*3,4*3*5,4*32,4*8*5) = 4.
%o (PARI) {m=1760;for(n=6,m, for(a=1,(n-3)\3, for(b=a+1,(n-a-1)\2,c=n-a-b;d=a*b*c%(a+b+c); if(c<d,if(a*b*d%(a+b+d) == c,if(a*c*d%(a+c+d) == b,if(b*c*d%(b+c+d) == a,print1(gcd(a,gcd(b,gcd(c,d))), ","))))))))}
%Y Cf. A092887, A092888, A092889, A092890.
%K nonn
%O 1,1
%A _Klaus Brockhaus_, Mar 12 2004