%I A000056
%S A000056 1,6,24,48,120,144,336,384,648,720,1320,1152,2184,2016,2880,
%T A000056 3072,4896,3888,6840,5760,8064,7920,12144,9216,15000,13104,
%U A000056 17496,16128,24360,17280,29760,24576,31680,29376,40320,31104
%N A000056 Order of the group SL(2,Z_n).
%C A000056 The number of equivalence classes of matrices modulo n of integer matrices 
               with determinant 1 modulo n. - Michael Somos Mar 20 2004
%D A000056 T. M. Apostol, Modular Functions and Dirichlet Series in Number Theory, 
               Springer-Verlag, 1990, page 46.
%D A000056 B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, NY, 1974, 
               p. 75.
%H A000056 T. D. Noe, <a href="b000056.txt">Table of n, a(n) for n=1..1000</a>
%F A000056 Multiplicative with a(p^e) = (p^2-1)*p^(3e-2). - David W. Wilson (davidwwilson(AT)comcast.net), 
               Aug 01, 2001.
%F A000056 a(n) = A000252/phi(n), where phi is Euler totient function (cf. A000010). 
               - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 30 2001
%F A000056 a(n)=n*sum(d|n, d^2*mu(n/d))=n*A007434(n) where A007434 is the Jordan 
               function J_2(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 
               03 2003
%e A000056 a(2)=6 because [0,1;1,0],[0,1;1,1],[1,0;0,1],[1,0;1,1],[1,1;0,1],[1,1;
               1,0] are the six matrices modulo 2 with determinant 1 modulo 2.
%p A000056 proc(n) local b,d: b := n^3: for d from 1 to n do if irem(n,d) = 0 and 
               isprime(d) then b := b*(1-d^(-2)): fi: od: RETURN(b): end:
%t A000056 Table[ Fold[ If[ Mod[ n, #2 ]==0 && PrimeQ[ #2 ], #1*(1-1/#2^2), #1 ]&, 
               n^3, Range[ n ] ], {n, 1, 35} ]
%t A000056 Table[ n^3 Times@@(1-1/Select[ Range[ 1, n ], (Mod[ n, #1 ]==0&&PrimeQ[ 
               #1 ])& ]^2), {n, 1, 35} ]
%o A000056 (PARI) {a(n) = if( n<1, 0, n * sumdiv(n, d, d^2 * moebius(n / d)))} /
               /* Michael Soos Mar 05 2008 */
%Y A000056 Cf. A011785, A064767, A007434, A000252.
%Y A000056 Cf. A001766.
%Y A000056 Sequence in context: A002688 A083212 A120572 this_sequence A083170 A087081 
               A089973
%Y A000056 Adjacent sequences: A000053 A000054 A000055 this_sequence A000057 A000058 
               A000059
%K A000056 nonn,easy,mult
%O A000056 1,2
%A A000056 N. J. A. Sloane (njas(AT)research.att.com).
%E A000056 Mathematica Program Aug 15 1997 (Olivier Gerard).