# 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