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A262354 a(n) is the number of 2 X 2 matrices over Z_p with determinant in {1,-1} where p = prime(n). 0
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 (list; graph; refs; listen; history; text; internal format)
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) print [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: A208536 A253947 A260344 * A052771 A056289 A056284

Adjacent sequences:  A262351 A262352 A262353 * A262355 A262356 A262357

KEYWORD

nonn

AUTHOR

Tom Edgar, Mar 24 2016

STATUS

approved

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Last modified October 21 18:43 EDT 2019. Contains 328308 sequences. (Running on oeis4.)