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

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..100

Formula

a(n) = Sum_{k=1..A316563(n)} 1/phi(A316564(n, k)).

Example

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]

Prog

(GAP) Concatenation([1], List([2..10], n->Sum( Filtered( ConjugacyClassesSubgroups( SL(2, Integers mod n)), x->IsCyclic( Representative(x))), Size)));
(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)))))))}

Crossrefs

Cf. A000056, A062314, A316536, A316553, A316560, A316563, A316564.

Sequence in context: A248860 A185039 A344521 * A175254 A211636 A294172

Adjacent sequences: A316534 A316535 A316536 * A316538 A316539 A316540

Keyword

nonn

Author

Andrew Howroyd, Jul 06 2018

Status

approved