%I A027375
%S A027375 0,2,2,6,12,30,54,126,240,504,990,2046,4020,8190,16254,32730,65280,
%T A027375 131070,261576,524286,1047540,2097018,4192254,8388606,16772880,33554400,
%U A027375 67100670,134217216,268419060,536870910,1073708010,2147483646,4294901760
%N A027375 Number of aperiodic binary strings of length n; also number of binary 
               sequences with primitive period n.
%C A027375 Equivalently, number of output sequences with primitive period n from 
               a simple cycling shift register.
%C A027375 Also, the number of nonempty subsets A of the set of the integers 1 to 
               n such that gcd(A) is relatively prime to n (for n>=1). - R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), Aug 13 2006
%D A027375 E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, NY, 1968, p. 84.
%D A027375 E. N. Gilbert and J. Riordan, Symmetry types of periodic sequences, Illinois 
               J. Math., 5 (1961), 657-665.
%D A027375 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%H A027375 T. D. Noe, <a href="b027375.txt">Table of n, a(n) for n=0..300</a>
%H A027375 J.-P. Allouche, <a href="http://www.lri.fr/~allouche/bibliorecente.html">
               Note on the transcendence of a generating function</a>. In A. Laurincikas 
               and E. Manstavicius, editors, Proceedings of the Palanga Conference 
               for the 75th birthday of Prof. Kubilius, New trends in Probab. and 
               Statist., Vol. 4, pages 461-465, 1997.
%H A027375 M. B. Nathanson, <a href="http://www.arXiv.org/abs/math.NT/0608150">Primitive 
               sets and and Euler phi function for subsets of {1,2,...,n}</a>, math.NT/
               0608150
%H A027375 P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/
               Publications/books.html">Analytic Combinatorics</a>, 2009; see page 
               85
%F A027375 Sum mu(d)*2^(n/d); d divides n.
%F A027375 A027375(p)=A000225(p)-1 if p is a prime number. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Aug 13 2006
%e A027375 a(3) = 6 = |{ 001, 010, 001, 011, 010, 110 }|
%t A027375 Table[ Apply[ Plus, MoebiusMu[ n / Divisors[n] ]*2^Divisors[n] ], {n, 
               1, 32} ]
%Y A027375 Essentially the same as A038199. Equals n*A001037(n).
%Y A027375 Cf. A056267.
%Y A027375 Cf. A020921.
%Y A027375 Sequence in context: A019311 A052994 A088219 this_sequence A059727 A103872 
               A159322
%Y A027375 Adjacent sequences: A027372 A027373 A027374 this_sequence A027376 A027377 
               A027378
%K A027375 nonn,nice,easy
%O A027375 0,2
%A A027375 N. J. A. Sloane (njas(AT)research.att.com).
%E A027375 Comments from Frank Ruskey (fruskey(AT)cs.uvic.ca), Jan 17 2000