A316563 Maximum order of an element in the special linear group SL(2, Z(n)).

1, 3, 6, 6, 10, 12, 14, 8, 18, 30, 22, 12, 26, 42, 30, 16, 34, 18, 38, 30, 42, 66, 46, 24, 50, 78, 54, 42, 58, 60, 62, 32, 66, 102, 70, 36, 74, 114, 78, 40, 82, 84, 86, 66, 90, 138, 94, 48, 98, 150, 102, 78, 106, 54, 110, 56, 114, 174, 118, 60, 122, 186, 126

Offset: 1

Author

Andrew Howroyd, Jul 06 2018

Keywords

• nonn

Links

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

Crossrefs

Row lengths of A316564.

Cf. A000056, A316537, A316565.

Programs

GAP

Concatenation([1], List([2..15], n->Maximum(List(SL(2, Integers mod n), Order))));

PARI

MatOrder(M)={my(id=matid(#M), k=1, N=M); while(N<>id, k++;N=N*M); k}
a(n)={my(m=0); for(a=0, n-1, for(b=0, n-1, for(c=0, n-1, for(d=0, n-1, my(M=Mod([a, b; c, d], n)); if(matdet(M)==1, m=max(m, MatOrder(M))))))); m}