cp's OEIS Frontend

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.

A060477 Number of orbits of length n in map whose periodic points are A000051.

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%I A060477 #22 Jan 05 2025 19:51:36
%S A060477 3,1,2,3,6,9,18,30,56,99,186,335,630,1161,2182,4080,7710,14532,27594,
%T A060477 52377,99858,190557,364722,698870,1342176,2580795,4971008,9586395,
%U A060477 18512790,35790267,69273666,134215680,260300986,505286415,981706806,1908866960,3714566310
%N A060477 Number of orbits of length n in map whose periodic points are A000051.
%H A060477 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 A060477 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 A060477 a(n) = (1/n)* Sum_{d|n} mu(d)*A000051(n/d).
%e A060477 a(3)=2 since the 3rd term of A000051 is 9 and the first term is 3.
%o A060477 (PARI) a000051(n) = 2^n+1;
%o A060477 a(n) = (1/n)*sumdiv(n, d, moebius(d)*a000051(n/d)); \\ _Michel Marcus_, Sep 11 2017
%o A060477 (Python)
%o A060477 from sympy import mobius, divisors
%o A060477 def A060477(n): return sum(mobius(n//d)*(2**d+1) for d in divisors(n,generator=True))//n # _Chai Wah Wu_, Feb 03 2022
%Y A060477 Cf. A000051.
%Y A060477 Cf. A001037, A059966 (both nearly identical to this sequence).
%Y A060477 Cf. A093210.
%K A060477 easy,nonn
%O A060477 1,1
%A A060477 _Thomas Ward_
%E A060477 A048578 replaced by A000051 in name and formula by _Michel Marcus_, Sep 11 2017