This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A270775 #9 Mar 31 2025 14:27:46 %S A270775 2,12,80,252,1100,1872,4352,6156,11132,22736,27900,47952,65600,75852, %T A270775 99452,143312,198476,219600,291852,347900,378432,480636,558092,689216, %U A270775 893952,1010000,1071612,1202252,1271376,1417472,2016252,2213900,2533952,2647116,3263696 %N A270775 a(n) is the number of invertible 2 X 2 upper triangular matrices over Z_p where p = prime(n). %C A270775 a(n) divides A244509(n). %H A270775 Gregor Olsavsky, <a href="http://www.jstor.org/stable/2690952">Groups formed from 2 X 2 matrices over Z_p</a>, Mathematics Magazine, Vol. 63, No. 4 (Oct., 1990), pp. 269-272. %F A270775 a(n) = p*(p-1)^2 where p = prime(n). %F A270775 Sum 1/a(n) = A382552. - _R. J. Mathar_, Mar 31 2025 %e A270775 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. %o A270775 (Sage) [nth_prime(p)*(nth_prime(p)-1)^2 for p in [1..35]] %Y A270775 Cf. A244509, A127917, A117762. %K A270775 nonn %O A270775 1,1 %A A270775 _Tom Edgar_, Mar 22 2016