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 A320095 Number of primitive (=aperiodic) n-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, 2, 11, 79, 773, 9281, 137191, 2396150, 48426649, 1111099879, 28531150811, 810554312866, 25239591811405, 854769747700454, 31278135014945519, 1229782937960902111, 51702516367459973873, 2314494592652832016030, 109912203092221714132219, 5518821052631039996623577 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..387 FORMULA a(n) = Sum_{j=1..n} Sum_{d|j} n^(d-1) * mu(j/d). a(n) = A143327(n,n). a(n) = Sum_{j=1..n} A143325(j,n). a(n) = A143326(n,n) / n. a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} mu(k) * x^k / (1 - n*x^k). - Ilya Gutkovskiy, Feb 16 2020 MAPLE b:= (n, k)-> add(`if`(d=n, k^(n-1), -b(d, k)), d=numtheory[divisors](n)): g:= proc(n, k) option remember; b(n, k)+`if`(n<2, 0, g(n-1, k)) end: a:= n-> g(n\$2): seq(a(n), n=1..23); MATHEMATICA a[n_] := Sum[n^(d-1)*MoebiusMu[j/d], {j, 1, n}, {d, Divisors[j]}]; Table[a[n], {n, 1, 20}] (* Jean-François Alcover, Oct 25 2022, after A143327 *) PROG (PARI) a(n) = sum(j=1, n, sumdiv(j, d, n^(d-1) * moebius(j/d))); \\ Michel Marcus, Feb 16 2020 CROSSREFS Main diagonal of A143327. Cf. A143325, A143326. Sequence in context: A253256 A163203 A142722 * A099661 A027110 A341955 Adjacent sequences: A320092 A320093 A320094 * A320096 A320097 A320098 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 05 2018 STATUS approved

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Last modified September 19 09:46 EDT 2024. Contains 376008 sequences. (Running on oeis4.)