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 A320090 Number of primitive (=aperiodic) 6-ary 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, 6, 41, 251, 1546, 9281, 55936, 335656, 2015236, 12091631, 72557806, 435346876, 2612129211, 15672776566, 94036939331, 564221643971, 3385331551426, 20311989308806, 121871945977221, 731231675909811, 4387390115926096, 26324340695837771, 157946044538104906 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1285 FORMULA a(n) = Sum_{j=1..n} Sum_{d|j} 6^(d-1) * mu(j/d). a(n) = A143327(n,6). a(n) = Sum_{j=1..n} A143325(j,6). a(n) = A143326(n,6) / 6. G.f.: (1/(1 - x)) * Sum_{k>=1} mu(k) * x^k / (1 - 6*x^k). - Ilya Gutkovskiy, Dec 11 2020 MAPLE b:= n-> add(`if`(d=n, 6^(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 - 6*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, 6^(d-1)*moebius(j/d))); \\ Michel Marcus, Dec 11 2020 CROSSREFS Column k=6 of A143327. Partial sums of A320071. Cf. A008683, A143325, A143326. Sequence in context: A197196 A295117 A198795 * A266425 A194781 A323969 Adjacent sequences: A320087 A320088 A320089 * A320091 A320092 A320093 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 05 2018 STATUS approved

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Last modified September 19 16:10 EDT 2024. Contains 376013 sequences. (Running on oeis4.)