A316537 Number of cyclic subgroups of the group SL(2, Z(n)), counting conjugates as distinct.
1, 5, 13, 28, 49, 73, 116, 176, 202, 265, 378, 464, 550, 636, 842, 936, 1041, 1183, 1486, 1712, 2082, 2055, 2120, 3088, 2114, 3023, 2503, 4200, 4238, 4862, 4902, 4648, 6564, 5749, 7434, 7688, 6331, 8190, 9880, 11344, 10172, 12066, 9378, 13224, 14168, 11612
Offset: 1
Keywords
Examples
Case n=2: generators of the 5 cyclic groups are: [ 1 0 ] [0 1] [1 0] [1 1] [0 1] [ 0 1 ] [1 0] [1 1] [0 1] [1 1]
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..100
Programs
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GAP
Concatenation([1], List([2..10], n->Sum( Filtered( ConjugacyClassesSubgroups( SL(2, Integers mod n)), x->IsCyclic( Representative(x))), Size)));
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PARI
MatOrder(M)={my(id=matid(#M), k=1, N=M); while(N<>id, k++;N=N*M); k} 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)))))))}