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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.
3
1, 10, 109, 1099, 11098, 110989, 1110988, 11109988, 111109888, 1111099879, 11111099878, 111110998888, 1111110998887, 11111109998878, 111111109988779, 1111111099988779, 11111111099988778, 111111110999888878, 1111111110999888877, 11111111109999887887
OFFSET
1,2
LINKS
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.
Sequence in context: A291894 A217322 A198700 * A267280 A015591 A078922
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 05 2018
STATUS
approved