cp's OEIS Frontend

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.

%I A320094 #9 Dec 11 2020 10:56:29
%S A320094 1,10,109,1099,11098,110989,1110988,11109988,111109888,1111099879,
%T A320094 11111099878,111110998888,1111110998887,11111109998878,
%U A320094 111111109988779,1111111099988779,11111111099988778,111111110999888878,1111111110999888877,11111111109999887887
%N 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.
%H A320094 Alois P. Heinz, <a href="/A320094/b320094.txt">Table of n, a(n) for n = 1..1000</a>
%F A320094 a(n) = Sum_{j=1..n} Sum_{d|j} 10^(d-1) * mu(j/d).
%F A320094 a(n) = A143327(n,10).
%F A320094 a(n) = Sum_{j=1..n} A143325(j,10).
%F A320094 a(n) = A143326(n,10) / 10.
%F A320094 G.f.: (1/(1 - x)) * Sum_{k>=1} mu(k) * x^k / (1 - 10*x^k). - _Ilya Gutkovskiy_, Dec 11 2020
%p A320094 b:= n-> add(`if`(d=n, 10^(n-1), -b(d)), d=numtheory[divisors](n)):
%p A320094 a:= proc(n) option remember; b(n)+`if`(n<2, 0, a(n-1)) end:
%p A320094 seq(a(n), n=1..30);
%o A320094 (PARI) a(n) = sum(j=1, n, sumdiv(j, d, 10^(d-1)*moebius(j/d))); \\ _Michel Marcus_, Dec 11 2020
%Y A320094 Column k=10 of A143327.
%Y A320094 Partial sums of A320075.
%Y A320094 Cf. A008683, A143325, A143326.
%K A320094 nonn
%O A320094 1,2
%A A320094 _Alois P. Heinz_, Oct 05 2018