[seqfan] Representing pairs of coprime integers

Charles Greathouse charles.greathouse at case.edu
Tue Jun 28 22:13:04 CEST 2011

I read a recent paper of Tripathi, which led me to read the earlier
papers of Brown & Shiue and Rødseth. These give results on Sylvester's
Frobenius problem: calculating the sum of numbers not of the form ax +
by for coprime a and b and nonnegative x and y as well as the sums of
higher powers.

A quick search didn't find anything in the OEIS, so I thought I'd add
entries.  But I'm not sure what the best way is.  If I was listing
pairs of numbers I would read the infinite table by antidiagonals.
Since (a, b) and (b, a) give the same results perhaps reading across
the resulting triangle would be better.  Should I just skip entries
where the two share a common factor, or is there a more natural
convention?  What is done in other entries (whose existence I posit)?

Charles Greathouse
Case Western Reserve University

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