

A062771


Order of automorphism group of the group C_n X C_2 (where C_n is the cyclic group with n elements).


2



1, 6, 2, 8, 4, 12, 6, 16, 6, 24, 10, 16, 12, 36, 8, 32, 16, 36, 18, 32, 12, 60, 22, 32, 20, 72, 18, 48, 28, 48, 30, 64, 20, 96, 24, 48, 36, 108, 24, 64, 40, 72, 42, 80, 24, 132, 46, 64, 42, 120, 32, 96, 52, 108, 40, 96, 36, 168, 58, 64, 60, 180, 36, 128, 48, 120, 66, 128, 44
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Multiplicative with a(2) = 6, a(2^e) = 2^(e+1), e>1, a(p^e) = (p1)*p^(e1), p>2.  Christian G. Bower, May 18 2005


LINKS

Table of n, a(n) for n=1..69.


FORMULA

For odd n: a(n) = phi(n) (sequence A000010).
Conjecture: a(n) = 6*phi(n) if n mod 4 = 2 and a(n) = 4*phi(n) if n mod 4 = 0.  Vladeta Jovovic, Jul 20 2001
Conjecture confirmed.  Christian G. Bower, May 20 2005


MATHEMATICA

a[n_] := Switch[Mod[n, 4], 0, 4, 2, 6, _, 1]*EulerPhi[n];
Array[a, 69] (* JeanFrançois Alcover, Apr 19 2018 *)


CROSSREFS

Sequence in context: A082577 A098686 A079718 * A249919 A254868 A071874
Adjacent sequences: A062768 A062769 A062770 * A062772 A062773 A062774


KEYWORD

nonn,mult


AUTHOR

Ahmed Fares (ahmedfares(AT)mydeja.com), Jul 18 2001


EXTENSIONS

More terms from Christian G. Bower, May 20 2005


STATUS

approved



