A071118 Size of the automorphism group of the group Z X Z_n.

2, 4, 12, 16, 40, 24, 84, 64, 108, 80, 220, 96, 312, 168, 240, 256, 544, 216, 684, 320, 504, 440, 1012, 384, 1000, 624, 972, 672, 1624, 480, 1860, 1024, 1320, 1088, 1680, 864, 2664, 1368, 1872, 1280, 3280, 1008, 3612, 1760, 2160, 2024, 4324, 1536

Offset: 1

Author

Sharon Sela (sharonsela(AT)hotmail.com), May 28 2002

Keywords

• nonn

Comments

This automorphism group is isomorphic to Z_2 X G where G is the group described in A002618.

Crossrefs

Cf. A002618, A000010.

Programs

Maple

with(numtheory); A071118:=n->2*n*phi(n); seq(A071118(n), n=1..40); # Wesley Ivan Hurt, Feb 11 2014

Mathematica

Table[ 2n*EulerPhi[n], {n, 1, 45}]

PARI

for(n=1,100,print1(2*n*eulerphi(n),","))

Formula

a(n) = 2 * A002618(n) = 2 * n * Phi(n).

Extensions

Edited by Robert G. Wilson v and Benoit Cloitre, May 28 2002