OFFSET
1,1
COMMENTS
The single group of prime order p has an automorphism group of order p-1. a(n) is a generalization of this.
EXAMPLE
3 is a term since |Aut(C3)|/GCD(|Aut(C3)|,3) = 2 and 3/GCD(|Aut(C3)|,3) = 3.
40 is a term since |Aut(C5xD8)|/GCD(|Aut(C5xD8)|,40) = 4 and 40/GCD(|Aut(C5xD8)|,40) = 5.
PROG
(GAP)
S:=[];;
for n in [1..30] do
for i in [1..NrSmallGroups(n)] do
Aut:=Order(AutomorphismGroup(SmallGroup(n, i)));;
if Aut/GCD_INT(n, Aut)=(n/GCD_INT(n, Aut))-1 then
S:=Concatenation(S, [n]);
break;
fi;
od;
od;
Print(S);
CROSSREFS
KEYWORD
nonn
AUTHOR
Miles Englezou, Jul 15 2024
STATUS
approved