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%I #24 Oct 03 2022 08:45:59
%S 1,2,2,2,4,2,4,4,4,2,4,2,6,4,2,4,12,12,48,48,48,12,48,24,24,12,12,12,
%T 48,48,240,480,240,96,96,96,480,288,192,192,960,960,5760,2880,2880,
%U 1440,8640,4320,4320,4320,2880,2880,20160,20160,10080,10080,10080,2880,20160,20160,161280,60480,60480,120960,241920,120960
%N Size of the automorphism group for the underlying graph of the divisibility graph of size n.
%C Define a graph H_n with the natural numbers 1,2,...,n as vertices and edges as follows: For any two vertices, v_1, v_2, there is an edge between v_1 and v_2 if there exists a natural number m > 1 such that v_1 = m * v_2. Thus an edge exists between v_1 and v_2 if v_2 divides v_1. a(n) is the size of the automorphism group on the vertices of H_n.
%C The first few terms (10) are easy to check on paper. For larger values the implementation of BLISS in the R package igraph was used.
%H Kevin Ryde, <a href="/A356831/b356831.txt">Table of n, a(n) for n = 1..1000</a>
%H Kevin Ryde, <a href="/A356831/a356831.c.txt">C Code using Nauty and GNU MP</a>
%o (C) See links.
%K nonn
%O 1,2
%A _Nils Gaute Voll_, Aug 30 2022
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