Conference rusure::math

269.0. "A funny sequence" by HARE::STAN () Mon Apr 29 1985 14:48

I was interested in finding the number of (unordered) triples, {p,q,r}
of integers, with the following properties:

	p > 0			q > 0			r > 0

	p < 2g+3		q < 2g+3		r < 2g+3

	pq | p+q+r+2g-2		qr | p+q+r+2g-2		rp | p+q+r+2g-2

where g is an integer larger than 0.
[x|y means x divides y.]

Let f(g) denote the number of such triples for a given value of g.

I wrote a computer program to tabulate the value of f(g).
The results are reported below:

  g    1   2   3   4   5   6   7   8   9  10  11  12  13  14  15
f(g)   5   7   8  11   8  13  11  11  13  17  11  17  13  15  17


  g   16  17  18  19  20  21  22  23  24  25  26  27  28  29  30
f(g)  18  12  18  18  19  18  19  11  22  19  19  21  23  14  23


I can see no pattern in the resulting sequence of numbers.  Can anyone help?
Note that there are sharp dips at g=5, 11, 17, 23, and 29.
I don't know if this is because these numbers are prime or if it's
something more mundane (like they differ by 6).