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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. 2
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.

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);

CROSSREFS

Main diagonal of A143327.

Sequence in context: A253256 A163203 A142722 * A099661 A027110 A118969

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 June 19 04:44 EDT 2019. Contains 324217 sequences. (Running on oeis4.)