# another reciprocal sum problem

ok we already know how to calculate how many rationals, $\mathbb{Q}$, exists in terms of the height function

$h(a/b)=\max (|a|,|b|)$

$gcd(a,b)=1$

It turns out that the A171503  entry of the OEIS tells more…

http://192.20.225.10/~njas/sequences/A171503

meanwhile it is natural to ask for convergence of

$1/3 + 1/7 + 1/15 + 1/23 + 1/31 + 1/47 + 1/71 + 1/87 + 1/111 + 1/127+...$

and for (non-) existence of a generating function…

The crescent sequence could be called Siehler’s numbers

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2 Comments

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### 2 responses to “another reciprocal sum problem”

1. to me it isn’t casual,
very probable this is known to specialist,
we can’t be too inocent to believe that we are the 1st to notice this…

2. It’s curious that I found the sequence looking for the number of rationals having height minor than N, while Siehler’s numbers are defined by the numbers of 2*2 integer matrices having determinant 1 and entries in {0,1,…,N}. Well, I could say that we find a different way to define the Siehler’s numbers