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A252764
Number of length n primitive (=aperiodic or period n) n-ary words.
3
1, 2, 24, 240, 3120, 46410, 823536, 16773120, 387419760, 9999899910, 285311670600, 8916097441680, 302875106592240, 11112006720144330, 437893890380096640, 18446744069414584320, 827240261886336764160, 39346408075098144278664, 1978419655660313589123960
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{d|n} n^d * mu(n/d), mu = A008683.
a(n) = A075147(n)*n.
a(n) = A074650(n,n) * n.
a(n) = A143325(n,n) * n.
a(n) = A143324(n,n).
EXAMPLE
a(3) = 24 because there are 24 primitive words of length 3 over 3-letter alphabet {a,b,c}: aab, aac, aba, abb, abc, aca, acb, acc, baa, bab, bac, bba, bbc, bca, bcb, bcc, caa, cab, cac, cba, cbb, cbc, cca, ccb.
MAPLE
with(numtheory):
a:= n-> add(n^d *mobius(n/d), d=divisors(n)):
seq(a(n), n=1..25);
MATHEMATICA
a[n_] := DivisorSum[n, n^# * MoebiusMu[n/#]& ];
Array[a, 25] (* Jean-François Alcover, Mar 24 2017, translated from Maple *)
CROSSREFS
Main diagonal of A143324.
Sequence in context: A143407 A366155 A228619 * A215929 A132596 A099669
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 21 2014
STATUS
approved