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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
OFFSET
1,2
LINKS
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.
Sequence in context: A197196 A295117 A198795 * A266425 A194781 A323969
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 05 2018
STATUS
approved