This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060172 #10 Jan 05 2025 19:51:36
%S A060172 1,1,1,2,3,6,9,19,28,62,93,205,315,703,1091,2440,3855,8616,13797,
%T A060172 30801,49929,111311,182361,405751,671088,1490409,2485504,5509504,
%U A060172 9256395,20480421,34636833,76499520,130150493,286960946,490853403,1080476338,1857283155,4081876927,7048151355
%N A060172 Number of orbits of length n under a map whose periodic points are counted by A027306.
%C A060172 The sequence A027306 records the number of points of period n under a map. The number of orbits of length n for this map gives the sequence above.
%H A060172 Y. Puri and T. Ward, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL4/WARD/short.html">Arithmetic and growth of periodic orbits</a>, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
%H A060172 Yash Puri and Thomas Ward, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/39-5/puri.pdf">A dynamical property unique to the Lucas sequence</a>, Fibonacci Quarterly, Volume 39, Number 5 (November 2001), pp. 398-402.
%F A060172 a(n) = (1/n)* Sum_{ d divides n } mu(d)*A027306(n/d).
%e A060172 u(7) = 9 since the map whose periodic points are counted by A027306 has 1 fixed point and 64 points of period 7, hence 9 orbits of length 7.
%o A060172 (PARI) a027306(n) = (2^n + if(n%2, 0, binomial(n, n/2)))/2;
%o A060172 a(n) = (1/n)*sumdiv(n, d, moebius(d)*a027306(n/d)); \\ _Michel Marcus_, Sep 11 2017
%Y A060172 Cf. A027306, A060164, A060165, A060166, A060167, A060168, A060169, A060170, A060171, A060173.
%K A060172 easy,nonn
%O A060172 1,4
%A A060172 _Thomas Ward_, Mar 13 2001
%E A060172 More terms from _Michel Marcus_, Sep 11 2017