A262354 a(n) is the number of 2 X 2 matrices over Z_p with determinant in {1,-1} where p = prime(n).

6, 48, 240, 672, 2640, 4368, 9792, 13680, 24288, 48720, 59520, 101232, 137760, 158928, 207552, 297648, 410640, 453840, 601392, 715680, 777888, 985920, 1143408, 1409760, 1825152, 2060400, 2185248, 2449872, 2589840, 2885568, 4096512, 4495920, 5142432, 5370960

Offset

1,1

Comments

a(n) divides A244509(n).

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

Links

Table of n, a(n) for n=1..34.

Gregor Olsavsky, Groups formed from 2 X 2 matrices over Z_p, Mathematics Magazine, Vol. 63, No. 4 (Oct., 1990), pp. 269-272.

Formula

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

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

Mathematica

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 *)

Prog

(Sage) [6] + [2*p*(p^2-1) for p in prime_range(3, 150)]
(PARI) lista(nn) = {print1(6, ", "); forprime(p=3, nn, print1(2*p*(p^2-1), ", ")); } \\ Altug Alkan, Mar 24 2016

Crossrefs

Cf. A244509, A127917, A117762, A270775.

Sequence in context: A253947 A260344 A353247 * A052771 A056289 A056284

Adjacent sequences: A262351 A262352 A262353 * A262355 A262356 A262357

Keyword

nonn

Author

Tom Edgar, Mar 24 2016

Status

approved