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A060220
Number of orbits of length n under the full 17-shift (whose periodic points are counted by A001026).
2
17, 136, 1632, 20808, 283968, 4022064, 58619808, 871959240, 13176430176, 201599248032, 3115626937056, 48551851084080, 761890617915840, 12026987582075856, 190828203433892736, 3041324491793194440, 48661191875666868480, 781282469552728498992, 12582759772902701307744
OFFSET
1,1
COMMENTS
Number of monic irreducible polynomials of degree n over GF(17). - Andrew Howroyd, Dec 10 2017
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)*A001026(n/d).
G.f.: Sum_{k>=1} mu(k)*log(1/(1 - 17*x^k))/k. - Ilya Gutkovskiy, May 20 2019
EXAMPLE
a(2)=136 since there are 289 points of period 2 in the full 17-shift and 17 fixed points, so there must be (289-17)/2 = 136 orbits of length 2.
MATHEMATICA
A060220[n_]:= DivisorSum[n, (17)^(n/#)*MoebiusMu[#] &]/n;
Table[A060220[n], {n, 40}] (* G. C. Greubel, Sep 13 2024 *)
PROG
(PARI) a001024(n) = 17^n;
a(n) = (1/n)*sumdiv(n, d, moebius(d)*a001024(n/d)); \\ Michel Marcus, Sep 11 2017
(Magma)
A060220:= func< n | (1/n)*(&+[MoebiusMu(d)*(17)^Floor(n/d): d in Divisors(n)]) >;
[A060220(n): n in [1..40]]; // G. C. Greubel, Sep 13 2024
(SageMath)
def A060220(n): return (1/n)*sum(moebius(k)*(17)^(n/k) for k in (1..n) if (k).divides(n))
[A060220(n) for n in range(1, 41)] # G. C. Greubel, Sep 13 2024
CROSSREFS
Column 17 of A074650.
Sequence in context: A010933 A022612 A205815 * A041550 A142788 A361150
KEYWORD
easy,nonn
AUTHOR
Thomas Ward, Mar 21 2001
EXTENSIONS
More terms from Michel Marcus, Sep 11 2017
STATUS
approved