# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a316537 Showing 1-1 of 1 %I A316537 #13 Jul 10 2018 18:43:23 %S A316537 1,5,13,28,49,73,116,176,202,265,378,464,550,636,842,936,1041,1183, %T A316537 1486,1712,2082,2055,2120,3088,2114,3023,2503,4200,4238,4862,4902, %U A316537 4648,6564,5749,7434,7688,6331,8190,9880,11344,10172,12066,9378,13224,14168,11612 %N A316537 Number of cyclic subgroups of the group SL(2, Z(n)), counting conjugates as distinct. %H A316537 Andrew Howroyd, Table of n, a(n) for n = 1..100 %F A316537 a(n) = Sum_{k=1..A316563(n)} 1/phi(A316564(n, k)). %e A316537 Case n=2: generators of the 5 cyclic groups are: %e A316537 [ 1 0 ] [0 1] [1 0] [1 1] [0 1] %e A316537 [ 0 1 ] [1 0] [1 1] [0 1] [1 1] %o A316537 (GAP) Concatenation([1], List([2..10], n->Sum( Filtered( ConjugacyClassesSubgroups( SL(2, Integers mod n)), x->IsCyclic( Representative(x))), Size))); %o A316537 (PARI) %o A316537 MatOrder(M)={my(id=matid(#M), k=1, N=M); while(N<>id, k++;N=N*M); k} %o A316537 a(n)={sum(a=0, n-1, sum(b=0, n-1, sum(c=0, n-1, sum(d=0, n-1, my(M=Mod([a, b; c, d], n)); if(matdet(M)==1, 1/eulerphi(MatOrder(M)))))))} %Y A316537 Cf. A000056, A062314, A316536, A316553, A316560, A316563, A316564. %K A316537 nonn %O A316537 1,2 %A A316537 _Andrew Howroyd_, Jul 06 2018 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE