Coprime Triples

Find the number of pairwise coprime triples of positive integers (a,b,c)(a,b,c) with a<b<c a < b < c such that

abc31,bca31 and cab31. a| bc-31, b|ca-31 \mbox{ and }c|ab-31.

Details and assumptions

The notation nm n \mid m means that nn is a divisor of mm.

Clarification: (ab31),(ac31),(ab-31), (ac-31), and (bc31)(bc-31) may be zero or negative.

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