%I #25 May 22 2020 05:11:05

%S 6,12,60,60,168,168,360,504,660,1092,2448,3420,4080,5616,6072,7800,

%T 9828,12180,14880,20160,20160,25308,32736,34440,39732,51888,58800,

%U 74412,102660,113460,150348,178920,194472,246480,262080,265680,285852,352440,372000,456288,515100,546312

%N Orders of the groups PSL(m,q) in increasing order as q runs through the prime powers (with repetitions).

%C 60 is the order of PSL(2,4) and of PSL(2,5).

%C 168 is the order of PSL(2,7) and of PSL(3,2).

%C 20160 is the order of PSL(4,2) and of PSL(3,4).

%C Other repetitions > 20160 for PSL(m,q) groups are not known.

%C See A334884 and A334994 for variations of this sequence.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Projective_linear_group">Projective linear group</a>.

%H <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Gre#groups">Index entries for sequences related to groups</a>.

%F #PSL(m,q) = (Product_{j=0..m-2} (q^m - q^j)) * q^(m-1) / gcd(m,q-1). - _Bernard Schott_, May 19 2020

%e a(5) = #PSL(2,7) = (7^2-1)*7/gcd(2,6) = 168, and,

%e a(6) = #PSL(3,2) = (2^3-1)*(2^3-2)*2^2/gcd(3,1) = 168.

%Y Cf. A002884 \ {1} (PSL(n,2)), A117762 (PSL(2, prime(n))).

%Y Cf. A334884 (another case with repetitions), A334994 (without repetitions).

%K nonn

%O 1,1

%A _Michel Marcus_, May 19 2020