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A320087
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Number of primitive (=aperiodic) ternary words with length less than or equal to n which are earlier in lexicographic order than any other word derived by cyclic shifts of the alphabet.
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3
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1, 3, 11, 35, 115, 347, 1075, 3235, 9787, 29387, 88435, 265315, 796755, 2390347, 7173227, 21519947, 64566667, 193700035, 581120523, 1743362283, 5230145947, 15690440099, 47071499707, 141214499227, 423644035627, 1270932113627, 3812797935395, 11438393826035
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OFFSET
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1,2
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..2096
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FORMULA
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a(n) = Sum_{j=1..n} Sum_{d|j} 3^(d-1) * mu(j/d).
a(n) = A143327(n,3).
a(n) = Sum_{j=1..n} A143325(j,3).
a(n) = A143326(n,3) / 3.
G.f.: (1/(1 - x)) * Sum_{k>=1} mu(k) * x^k / (1 - 3*x^k). - Ilya Gutkovskiy, Dec 11 2020
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MAPLE
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b:= n-> add(`if`(d=n, 3^(n-1), -b(d)), d=numtheory[divisors](n)):
a:= proc(n) option remember; b(n)+`if`(n<2, 0, a(n-1)) end:
seq(a(n), n=1..30);
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MATHEMATICA
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nmax = 20; Rest[CoefficientList[Series[1/(1-x) * Sum[MoebiusMu[k] * x^k / (1 - 3*x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Dec 11 2020 *)
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PROG
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(PARI) a(n) = sum(j=1, n, sumdiv(j, d, 3^(d-1)*moebius(j/d))); \\ Michel Marcus, Dec 11 2020
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CROSSREFS
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Column k=3 of A143327.
Partial sums of A034741.
Cf. A008683, A143325, A143326.
Sequence in context: A125672 A107683 A259400 * A014335 A147474 A247417
Adjacent sequences: A320084 A320085 A320086 * A320088 A320089 A320090
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Oct 05 2018
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STATUS
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approved
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