OFFSET
1,1
COMMENTS
For orders of Aut(SL_2(K)) = Aut(PGL_2(K)) = Aut(PSL_2(K)) see A352807.
See the Groupprops link for a formula for |Aut(GL(n,q))| in general.
LINKS
Jianing Song, Table of n, a(n) for n = 1..10000
FORMULA
For q = p^r, |Aut(GL(2,q))| = r*q*(q^2-1)*eulerphi(2*(q-1)) = |PGammaL(2,q)|*eulerphi(2*(q-1)) (see A352807). In general, we have |Aut(GL(n,q))|/|Aut(SL(n,q))| = eulerphi(n*(q-1))/eulerphi(n).
EXAMPLE
PROG
(PARI) [(q+1)*q*(q-1)*isprimepower(q)*eulerphi(2*(q-1)) | q <- [1..200], isprimepower(q)]
CROSSREFS
KEYWORD
nonn
AUTHOR
Jianing Song, Apr 08 2022
STATUS
approved