login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A053191 a(n) = n^2 * phi(n). 19
1, 4, 18, 32, 100, 72, 294, 256, 486, 400, 1210, 576, 2028, 1176, 1800, 2048, 4624, 1944, 6498, 3200, 5292, 4840, 11638, 4608, 12500, 8112, 13122, 9408, 23548, 7200, 28830, 16384, 21780, 18496, 29400, 15552, 49284, 25992, 36504, 25600, 67240 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Number of invertible 2 X 2 symmetric matrices over Z(n). - T. D. Noe, 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, 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

LINKS

Table of n, a(n) for n=1..41.

FORMULA

a(n) = n^2 * phi(n) = A000010(n^3).

Dirichlet g.f.: zeta(s-3)/zeta(s-2). - R. J. Mathar, Feb 09 2011

EXAMPLE

n=5: n^3=125, EulerPhi(125) = 125 - 25 = 100.

MAPLE

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

MATHEMATICA

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, Jan 13 2006 *)

Table[n^2*EulerPhi[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Nov 10 2009 *)

PROG

(Sage) [n^2*euler_phi(n) for n in xrange(1, 42)] # Zerinvary Lajos, Jun 06 2009

(MAGMA) [ n^2*EulerPhi(n) : n in [1..100] ]; // Vincenzo Librandi, Apr 21 2011

(PARI) a(n) = n^2*eulerphi(n); \\ Michel Marcus, Oct 31 2017

CROSSREFS

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: A049726 A130656 A292161 * A003474 A095823 A092116

Adjacent sequences:  A053188 A053189 A053190 * A053192 A053193 A053194

KEYWORD

nonn,mult

AUTHOR

Labos Elemer, Mar 02 2000

EXTENSIONS

Edited by N. J. A. Sloane at the suggestion of Andrew Plewe, Jun 05 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 22 15:27 EST 2017. Contains 295089 sequences.