This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A216766 #18 May 05 2022 07:25:57
%S A216766 1,14,37,719,5056,151513,1759463,68163191,352149277,360867217,
%T A216766 15078888947,1546201093747,95491548878617,10736398220663,
%U A216766 1400899861968427,41036431877859203,41386424246755373,8212624279323157381,256265816149636840711,29139716513641120366493
%N A216766 Numerators of partial sums of 1/A216765(n).
%C A216766 Partial sums of the reciprocals of (perfect powers -- squares, cubes, etc. -- plus 1).
%H A216766 Amiram Eldar, <a href="/A216766/b216766.txt">Table of n, a(n) for n = 1..420</a>
%F A216766 a(n) = numerator(Sum_{k=1..n} 1/A216765(k)).
%F A216766 Limit_{n->oo} a(n)/A216767(n) = Pi^2/3 - 5/2. - _Amiram Eldar_, May 05 2022
%e A216766 The partial sums are of the sequence of fractions: 1/5 + 1/9 + 1/10 + 1/17 + 1/26 + 1/28 + 1/33 + 1/37 + 1/50, ... and thus the partial sums are 1/5, 14/45, 37/90, 719/1530, 5056/9995, 151513/278460, 1759463/3063060, 68163191/113333220, 352149277/566666100, 360867217/566666100, 15078888947/23233310100, ...
%t A216766 Numerator[FoldList[Plus, 1/(1 + Select[Range[250], GCD @@ FactorInteger[#][[;; , 2]] > 1 &])]] (* _Amiram Eldar_, May 05 2022 *)
%Y A216766 Cf. A001597, A045542, A175064, A214390, A214391, A216765, A216767 (denominators).
%K A216766 easy,nonn,frac
%O A216766 1,2
%A A216766 _Jonathan Vos Post_, Sep 15 2012