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 A344497 #17 Jun 15 2021 07:12:17
%S A344497 0,1,1,2,2,3,3,3,4,5,5,5,5,6,7,7,7,8,8,8,9,10,10,10,11,12,12,13,13,13,
%T A344497 13,14,14,15,16,16,16,17,17,18,18,19,19,19,20,21,21,21,21,22,23,23,23,
%U A344497 24,24,25,25,26,26,26,26,27,28,28,28,29,29,30,30,31,31
%N A344497 Matching number of the divisor graph of {1,...,n}.
%C A344497 a(n) is the matching number of the graph on vertices {1,...,n} in which two vertices are connected by an edge if one divides another.
%C A344497 The maximum matching in a graph can be calculated by the blossom algorithm.
%C A344497 By considering the matching k-2k with k = floor(n/4)+1,...,floor(n/2), we obtain the inequality: floor(n/4) <= a(n).
%H A344497 Paul Revenant, <a href="/A344497/b344497.txt">Table of n, a(n) for n = 1..8000</a>
%H A344497 Paul Revenant, <a href="https://perso.ens-lyon.fr/paul.revenant/Divisor_Graph/Matching_Divisor_Graph.cpp">C++ program using the Blossom algorithm</a>
%H A344497 Wikipedia, <a href="https://en.wikipedia.org/wiki/Matching_(graph_theory)">Matching (graph theory)</a>
%H A344497 Wikipedia, <a href="https://en.wikipedia.org/wiki/Blossom_algorithm">Blossom algorithm</a>
%F A344497 floor(n/4) <= a(n) <= floor(n/2).
%e A344497 a(10) = 5, since the divisor graph of {1,...,10} has a perfect matching: 1-7, 2-6, 3-9, 4-8, 5-10, which is a matching of size 5.
%o A344497 (C++) // program available at Revenant link
%Y A344497 Cf. A002265, A004526.
%K A344497 nonn
%O A344497 1,4
%A A344497 _Paul Revenant_, May 21 2021