A262354 - OEIS

%I #20 Mar 14 2020 10:32:08

%S 6,48,240,672,2640,4368,9792,13680,24288,48720,59520,101232,137760,

%T 158928,207552,297648,410640,453840,601392,715680,777888,985920,

%U 1143408,1409760,1825152,2060400,2185248,2449872,2589840,2885568,4096512,4495920,5142432,5370960

%N a(n) is the number of 2 X 2 matrices over Z_p with determinant in {1,-1} where p = prime(n).

%C a(n) divides A244509(n).

%C For n>2 (i.e. p=prime(n)>=5), a(n) gives the order of the largest proper subgroup of GL(2,Z_p).

%H Gregor Olsavsky, <a href="http://www.jstor.org/stable/2690952">Groups formed from 2 X 2 matrices over Z_p</a>, Mathematics Magazine, Vol. 63, No. 4 (Oct., 1990), pp. 269-272.

%F For n>1, a(n) = 2*p*(p^2-1) where p = prime(n).

%F For n>1, a(n) = 2*A127917(n).

%t Prepend[2 Table[(Prime@ n + 1) Prime@ n (Prime@ n - 1), {n, 2, 34}], 6] (* _Michael De Vlieger_, Mar 24 2016, after _Artur Jasinski_ at A127917 *)

%o (Sage) [6] + [2*p*(p^2-1) for p in prime_range(3,150)]

%o (PARI) lista(nn) = {print1(6, ", "); forprime(p=3, nn, print1(2*p*(p^2-1), ", ")); } \\ _Altug Alkan_, Mar 24 2016

%Y Cf. A244509, A127917, A117762, A270775.

%K nonn

%O 1,1

%A _Tom Edgar_, Mar 24 2016