1,2

The number of equivalence classes of matrices modulo n of integer matrices with determinant 1 modulo n. - Michael Somos Mar 20 2004

T. M. Apostol, Modular Functions and Dirichlet Series in Number Theory, Springer-Verlag, 1990, page 46.

B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, NY, 1974, p. 75.

T. D. Noe, Table of n, a(n) for n=1..1000

Multiplicative with a(p^e) = (p^2-1)*p^(3e-2). - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.

a(n) = A000252/phi(n), where phi is Euler totient function (cf. A000010). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 30 2001

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

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.

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:

Table[ Fold[ If[ Mod[ n, #2 ]==0 && PrimeQ[ #2 ], #1*(1-1/#2^2), #1 ]&, n^3, Range[ n ] ], {n, 1, 35} ]

Table[ n^3 Times@@(1-1/Select[ Range[ 1, n ], (Mod[ n, #1 ]==0&&PrimeQ[ #1 ])& ]^2), {n, 1, 35} ]

(PARI) {a(n) = if( n<1, 0, n * sumdiv(n, d, d^2 * moebius(n / d)))} //* Michael Soos Mar 05 2008 */

Cf. A011785, A064767, A007434, A000252.

Cf. A001766.

Sequence in context: A002688 A083212 A120572 this_sequence A083170 A087081 A089973

Adjacent sequences: A000053 A000054 A000055 this_sequence A000057 A000058 A000059

nonn,easy,mult

N. J. A. Sloane (njas(AT)research.att.com).

Mathematica Program Aug 15 1997 (Olivier Gerard).