A092891 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.

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, 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, 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

Offset

1,1

Comments

First, second, third and fourth component of the quadruples are resp. in A092887, A092888, A092889, A092890.

Links

Table of n, a(n) for n=1..93.

Example

The third quadruple is 12, 60, 128, 160, hence a(3) = gcd(4*3,4*3*5,4*32,4*8*5) = 4.

Prog

(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))), ", "))))))))}

Crossrefs

Cf. A092887, A092888, A092889, A092890.

Sequence in context: A145762 A024539 A128271 * A229484 A080212 A186727

Adjacent sequences: A092888 A092889 A092890 * A092892 A092893 A092894

Keyword

nonn

Author

Klaus Brockhaus, Mar 12 2004

Status

approved