The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A252764 Number of length n primitive (=aperiodic or period n) n-ary words. 2
 1, 2, 24, 240, 3120, 46410, 823536, 16773120, 387419760, 9999899910, 285311670600, 8916097441680, 302875106592240, 11112006720144330, 437893890380096640, 18446744069414584320, 827240261886336764160, 39346408075098144278664, 1978419655660313589123960 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..350 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. Cf. A008683, A074650, A075147, A143324, A143325. Sequence in context: A270564 A143407 A228619 * A215929 A132596 A099669 Adjacent sequences:  A252761 A252762 A252763 * A252765 A252766 A252767 KEYWORD nonn AUTHOR Alois P. Heinz, Dec 21 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 28 12:32 EDT 2020. Contains 334681 sequences. (Running on oeis4.)