A320094 Number of primitive (=aperiodic) 10-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.

1, 10, 109, 1099, 11098, 110989, 1110988, 11109988, 111109888, 1111099879, 11111099878, 111110998888, 1111110998887, 11111109998878, 111111109988779, 1111111099988779, 11111111099988778, 111111110999888878, 1111111110999888877, 11111111109999887887

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

a(n) = Sum_{j=1..n} Sum_{d|j} 10^(d-1) * mu(j/d).

a(n) = A143327(n,10).

a(n) = Sum_{j=1..n} A143325(j,10).

a(n) = A143326(n,10) / 10.

G.f.: (1/(1 - x)) * Sum_{k>=1} mu(k) * x^k / (1 - 10*x^k). - Ilya Gutkovskiy, Dec 11 2020

Maple

b:= n-> add(`if`(d=n, 10^(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);

Prog

(PARI) a(n) = sum(j=1, n, sumdiv(j, d, 10^(d-1)*moebius(j/d))); \\ Michel Marcus, Dec 11 2020

Crossrefs

Column k=10 of A143327.

Partial sums of A320075.

Cf. A008683, A143325, A143326.

Sequence in context: A291894 A217322 A198700 * A267280 A015591 A078922

Adjacent sequences: A320091 A320092 A320093 * A320095 A320096 A320097

Keyword

nonn

Author

Alois P. Heinz, Oct 05 2018

Status

approved