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
Keywords
Links
- Gregor Olsavsky, Groups formed from 2 X 2 matrices over Z_p, Mathematics Magazine, Vol. 63, No. 4 (Oct., 1990), pp. 269-272.
Programs
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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 *) -
PARI
lista(nn) = {print1(6, ", "); forprime(p=3, nn, print1(2*p*(p^2-1), ", ")); } \\ Altug Alkan, Mar 24 2016 -
Sage
[6] + [2*p*(p^2-1) for p in prime_range(3,150)]
Formula
For n>1, a(n) = 2*p*(p^2-1) where p = prime(n).
For n>1, a(n) = 2*A127917(n).
Comments