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The sum of thirteen positive integers is 79633. If placed appropriately on the vertices of this graph, two of them will be joined by an edge if and only if they have a common divisor greater than 1 (that is, they are not relatively prime). In non-decreasing order, what are those thirteen integers?

Snow Flake graph

Related problem: Labelling a Snow Flake Graph to Attain Minimum Sum


marked as duplicate by Dr Xorile, Glorfindel, QuantumTwinkie, Deusovi Feb 22 at 18:50

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    $\begingroup$ How can it be 79633 when the minimum from the linked problem was larger than that? I see that you say that the numbers are not necessarily distinct, but given the "if and only if" nature of the edges, equal numbers must be connected and have the same neighbours, and there are no such vertices in the graph. So the numbers must be distinct, just like in the other problem. $\endgroup$ – Jaap Scherphuis Feb 22 at 13:10
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    $\begingroup$ It would seem that Barrera has found a smaller labelling for the Snow Flake graph in question, so there might be a flaw in the argument proving hexomino´s labelling is minimum. Must wait and see! $\endgroup$ – Bernardo Recamán Santos Feb 22 at 14:31
  • $\begingroup$ @JaapScherphuis I think the flaw is with my result, I thought I had looked at all cases but it's possible there was a mistake in my code, currently looking into it. $\endgroup$ – hexomino Feb 22 at 15:59
  • $\begingroup$ @JaapScherphuis Yes the mistake was mine, apologies for misleading you. I've updated my answer with a smaller solution. I think the reasoning of Bass and 2012rcampion should still hold so the solution will be within this scope. $\endgroup$ – hexomino Feb 22 at 16:37
  • $\begingroup$ If the minimal attainable on the linked question turns out to actually be 79633, should this question be closed as a duplicate? Why did the OP not post his arrangement (assuming he has one) as an answer there? I have a feeling the OP intended this puzzle to be fundamentally different in some way, but I don't see it. $\endgroup$ – Jaap Scherphuis Feb 22 at 16:48