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 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

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