A060164 Number of orbits of length n under the map whose periodic points are counted by A000364.

1, 2, 20, 345, 10104, 450450, 28480140, 2423938845, 267208852820, 37037118818700, 6304443126648900, 1292877846962865230, 314390193022547991720, 89447117243116404721950, 29436259549934873636908816, 11094961973721205588579579845, 4748429366816935180127543967840

Offset: 1

Author

Thomas Ward, Mar 13 2001

Keywords

• easy
• nonn

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.

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..243
• 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.

Crossrefs

Cf. A000364, A060165, A060166, A060167, A060168, A060169, A060170, A060171, A060172, A060173.

Formula

a(n) = (1/n)* Sum_{d|n} mu(d)*A000364(n/d).