A316563 - OEIS

%I #9 Jul 10 2018 18:43:40

%S 1,3,6,6,10,12,14,8,18,30,22,12,26,42,30,16,34,18,38,30,42,66,46,24,

%T 50,78,54,42,58,60,62,32,66,102,70,36,74,114,78,40,82,84,86,66,90,138,

%U 94,48,98,150,102,78,106,54,110,56,114,174,118,60,122,186,126

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

%H Andrew Howroyd, <a href="/A316563/b316563.txt">Table of n, a(n) for n = 1..100</a>

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

%o (PARI)

%o MatOrder(M)={my(id=matid(#M), k=1, N=M); while(N<>id, k++;N=N*M); k}

%o 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}

%Y Row lengths of A316564.

%Y Cf. A000056, A316537, A316565.

%K nonn

%O 1,2

%A _Andrew Howroyd_, Jul 06 2018