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 A005417 Maximal period of an n-stage shift register. (Formerly M1587) 1
 2, 6, 12, 30, 60, 120, 210, 420, 840, 1260, 2520, 2520, 5040, 9240, 13860, 27720, 32760, 55440, 65520, 120120, 180180, 360360, 360360, 720720, 720720, 942480, 1113840 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Maximal order of an element of finite order in GL(2n, Z) or GL(2n+1, Z). a(n) is the max of the first n numbers in A080742. REFERENCES H. Lüneburg, Galoisfelder, Kreisteilungskörper und Schieberegisterfolgen. B. I. Wissenschaftsverlag, Mannheim, 1979. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS J. Kuzmanovich and A. Pavlichenkov, Finite groups of matrices whose entries are integers, Amer. Math. Monthly, 109 (2002), 173-186. FORMULA a(n) = max m such that A067240(m) <= 2n + 1. E.g., a(2) = 12 since 12 is largest m such that A067240(m) <= 5. MATHEMATICA (* b, c = a080737 *) nmax = 26; kmax = 1200000; (* kmax increased by 100000 until results do not change *) b[1] = b[2] = 0; b[p_?PrimeQ] := b[p] = p-1; b[k_] := b[k] = If[Length[f = FactorInteger[k]]==1, EulerPhi[k], Total[b /@ (f[[All, 1]]^f[[All, 2]])] ]; orders = Table[{k, b[k]}, {k, 1, kmax}]; c[0] = 2; c[n_] := c[n] = Select[orders, 2n-1 <= #[[2]] <= 2n&][[-1, 1]]; a[n_] := Table[c[m], {m, 0, n}] // Max; Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Dec 17 2017 *) CROSSREFS Cf. A000793, A080742, A080743. Sequence in context: A133996 A284573 A080742 * A058215 A330542 A166456 Adjacent sequences:  A005414 A005415 A005416 * A005418 A005419 A005420 KEYWORD nonn,nice,more AUTHOR EXTENSIONS Entry revised by N. J. A. Sloane, Mar 10 2002 STATUS approved

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Last modified September 18 17:02 EDT 2020. Contains 337170 sequences. (Running on oeis4.)