A270775 a(n) is the number of invertible 2 X 2 upper triangular matrices over Z_p where p = prime(n).
2, 12, 80, 252, 1100, 1872, 4352, 6156, 11132, 22736, 27900, 47952, 65600, 75852, 99452, 143312, 198476, 219600, 291852, 347900, 378432, 480636, 558092, 689216, 893952, 1010000, 1071612, 1202252, 1271376, 1417472, 2016252, 2213900, 2533952, 2647116, 3263696
Offset: 1
Keywords
Examples
Over Z_2, there are only two invertible upper triangular 2 X 2 matrices: [[1,0],[0,1]] and [[1,1],[0,1]] so a(1) = 2.
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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Sage
[nth_prime(p)*(nth_prime(p)-1)^2 for p in [1..35]]
Formula
a(n) = p*(p-1)^2 where p = prime(n).
Sum 1/a(n) = A382552. - R. J. Mathar, Mar 31 2025
Comments