A356831 Size of the automorphism group for the underlying graph of the divisibility graph of size n.

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, 48, 48, 240, 480, 240, 96, 96, 96, 480, 288, 192, 192, 960, 960, 5760, 2880, 2880, 1440, 8640, 4320, 4320, 4320, 2880, 2880, 20160, 20160, 10080, 10080, 10080, 2880, 20160, 20160, 161280, 60480, 60480, 120960, 241920, 120960

Offset

1,2

Comments

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.

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.

Links

Kevin Ryde, Table of n, a(n) for n = 1..1000

Kevin Ryde, C Code using Nauty and GNU MP

Prog

(C) See links.

Crossrefs

Sequence in context: A366438 A152674 A072056 * A066012 A063375 A064129

Adjacent sequences: A356828 A356829 A356830 * A356832 A356833 A356834

Keyword

nonn

Author

Nils Gaute Voll, Aug 30 2022

Status

approved