A316560 Number of cyclic subgroups of the group GL(2, Z(n)), counting conjugates as distinct.

1, 5, 28, 62, 176, 148, 610, 696, 1252, 920, 2296, 1972, 4874, 3523, 6040, 6320, 8136, 7348, 14984, 13568, 22124, 11920, 17396, 23952, 29846, 28172, 38044, 47656, 47282, 32908, 75036, 53520, 71768, 42312, 145852, 99892, 123524, 88456, 187036, 179200, 152290

Offset

1,2

Links

Table of n, a(n) for n=1..41.

Formula

a(n) = Sum_{k=1..A316565(n)} 1/phi(A316566(n,k)).

Prog

(GAP) Concatenation([1], List([2..7], n->Sum( Filtered( ConjugacyClassesSubgroups( GL(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(gcd(lift(matdet(M)), n)==1, 1/eulerphi(MatOrder(M)))))))}

Crossrefs

Cf. A053651, A066947, A316537, A316559, A316565, A316566.

Sequence in context: A341061 A161165 A063140 * A275709 A257093 A225261

Adjacent sequences: A316557 A316558 A316559 * A316561 A316562 A316563

Keyword

nonn

Author

Andrew Howroyd, Jul 06 2018

Status

approved