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

1,1

Comments

a(n) divides A244509(n).

Links

Table of n, a(n) for n=1..35.

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

Formula

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

Example

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.

Prog

(Sage) [nth_prime(p)*(nth_prime(p)-1)^2 for p in [1..35]]

Crossrefs

Cf. A244509, A127917, A117762.

Sequence in context: A227968 A289662 A107632 * A240836 A270919 A082142

Adjacent sequences: A270772 A270773 A270774 * A270776 A270777 A270778

Keyword

nonn

Author

Tom Edgar, Mar 22 2016

Status

approved