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 A060164 Number of orbits of length n under the map whose periodic points are counted by A000364. 9
 1, 2, 20, 345, 10104, 450450, 28480140, 2423938845, 267208852820, 37037118818700, 6304443126648900, 1292877846962865230, 314390193022547991720, 89447117243116404721950 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The sequence A000364 seems to record the number of points of period n under a map. The number of orbits of length n for this map gives the sequence above. LINKS Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1. Yash Puri and Thomas Ward, A dynamical property unique to the Lucas sequence, Fibonacci Quarterly, Volume 39, Number 5 (November 2001), pp. 398-402. FORMULA a(n) = (1/n)* Sum_{d|n} mu(d)*A000364(n/d). EXAMPLE u(3) = 20 since the conjectured map whose periodic points are counted by A000364 would have 1 fixed point and 61 points of period 3, so it must have 20 orbits of length 3. CROSSREFS Cf. A000364, A060165, A060166, A060167, A060168, A060169, A060170, A060171, A060172, A060173. Sequence in context: A128481 A177397 A104462 * A267827 A084948 A187661 Adjacent sequences:  A060161 A060162 A060163 * A060165 A060166 A060167 KEYWORD easy,nonn AUTHOR Thomas Ward (t.ward(AT)uea.ac.uk), Mar 13 2001 STATUS approved

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