

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
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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 5159.
A. Wilansky, Spectral decomposition of matrices for high school students, Math. Mag. 41 1968 5159. (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, n1, m[1, 1] = Mod(i, n); for (j=0, n1, m[1, 2] = Mod(j, n); for (k=0, n1, m[2, 1] = Mod(k, n); for (l=0, n1, 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



