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 A320087 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. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..2096 FORMULA 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 MAPLE 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); MATHEMATICA 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 *) PROG (PARI) a(n) = sum(j=1, n, sumdiv(j, d, 3^(d-1)*moebius(j/d))); \\ Michel Marcus, Dec 11 2020 CROSSREFS 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 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 05 2018 STATUS approved

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Last modified May 30 11:25 EDT 2023. Contains 363050 sequences. (Running on oeis4.)