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 A316537 Number of cyclic subgroups of the group SL(2, Z(n)), counting conjugates as distinct. 6
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified July 13 21:17 EDT 2024. Contains 374288 sequences. (Running on oeis4.)