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A092891
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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.
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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| First, second, third and fourth component of the quadruples are resp. in A092887, A092888, A092889, A092890.
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EXAMPLE
| The third quadruple is 12, 60, 128, 160, hence a(3) = gcd(4*3,4*3*5,4*32,4*8*5) = 4.
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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))), ", "))))))))}
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CROSSREFS
| Cf. A092887, A092888, A092889, A092890.
Sequence in context: A145762 A024539 A128271 * A080212 A186727 A145998
Adjacent sequences: A092888 A092889 A092890 * A092892 A092893 A092894
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KEYWORD
| nonn
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AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 12 2004
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