1,2

Number of invertible 2 X 2 symmetric matrices over Z(n). - T. D. Noe (noe(AT)sspectra.com), Jan 13 2006

Note that A115077 gives the number of 2 X 2 symmetric matrices having nonzero determinant. However for composite n a nonzero determinant is not sufficient for the matrix to be invertible; the determinant must also be relatively prime to n. - T. D. Noe (noe(AT)sspectra.com), Jan 13 2006

Also Euler phi function of n^3.

For n^k, EulerPhi[n^k]=n^(k-1)*EulerPhi[n]. The same holds if Phi is replaced by cototient function.

Also the sum of the degrees of the irreducible representations of the group GL(2,Z_n) (sequence A000252). - Sharon Sela (sharonsela(AT)hotmail.com), Feb 06 2002

a(n)=n^2*EulerPhi[n]=A000010(n^3)

n=5: n^3=125, EulerPhi[125]=125-25=100.

with(numtheory):a:=n->phi(n^3): seq(a(n), n=1..41); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 07 2007

Table[cnt=0; Do[m={{a, b}, {b, c}}; If[Det[m, Modulus->n]>0 && MatrixQ[Inverse[m, Modulus->n]], cnt++ ], {a, 0, n-1}, {b, 0, n-1}, {c, 0, n-1}]; cnt, {n, 2, 50}] - T. D. Noe (noe(AT)sspectra.com), Jan 13 2006

Table[EulerPhi[n^3], {n, 0, 40}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 10 2009]

(Other) sage: [euler_phi(n^3)for n in xrange(1, 42)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 06 2009]

Cf. A000252 (number of invertible 2 X 2 matrices over Z(n)), A115075, A115076, A115077.

Cf. A000010, A051953, A002618, A053650, A053191, A053192, A001248.

Sequence in context: A033166 A049726 A130656 this_sequence A003474 A095823 A092116

Adjacent sequences: A053188 A053189 A053190 this_sequence A053192 A053193 A053194

nonn,mult

Labos E. (labos(AT)ana.sote.hu), Mar 02 2000

Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, Jun 05 2007