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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A006045 Sum of orders of all 2 X 2 matrices with entries mod n.
(Formerly M3946)
2
1, 26, 272, 722, 5270, 5260, 37358, 18414, 56216, 95668, 487714, 99796, 1304262, 627046, 593398, 481982, 7044222, 931396, 11570384, 1602940, 4037650, 8694134, 40220524, 2069292, 15855230, 21686124, 13215872, 10948486, 129952894, 10451648 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The order of a matrix M over Z/(nZ) is the smallest k such that M^k is idempotent.

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Sean A. Irvine, Table of n, a(n) for n = 1..61

A. Wilansky, Spectral decomposition of matrices for high school students, Math. Mag. 41 1968 51-59.

A. Wilansky, Spectral decomposition of matrices for high school students, Math. Mag. 41 1968 51-59. (Annotated scanned copy)

A. Wilansky, Letters to N. J. A. Sloane, Jun. 1991

PROG

(PARI) order(m) = {kk = 1; ok = 0; while (! ok, mk = m^kk; if (mk^2 == mk, ok = 1, kk++); ); return(kk); }

a(n) = {ret = 0; m = matrix(2, 2); for (i=0, n-1, m[1, 1] = Mod(i, n); for (j=0, n-1, m[1, 2] = Mod(j, n); for (k=0, n-1, m[2, 1] = Mod(k, n); for (l=0, n-1, m[2, 2] = Mod(l, n); ret += order(m); ); ); ); ); return (ret); }

CROSSREFS

Sequence in context: A187695 A195755 A186261 * A022686 A200555 A130901

Adjacent sequences:  A006042 A006043 A006044 * A006046 A006047 A006048

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Albert Wilansky

EXTENSIONS

The article gives an incorrect value for a(5).

More terms from Michel Marcus, Jun 07 2013

More terms from Sean A. Irvine, Dec 18 2016

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 19 14:36 EDT 2019. Contains 328222 sequences. (Running on oeis4.)