%I A003277 M0650
%S A003277 1,2,3,5,7,11,13,15,17,19,23,29,31,33,35,37,41,43,47,51,53,59,61,65,
%T A003277 67,69,71,73,77,79,83,85,87,89,91,95,97,101,103,107,109,113,115,119,
%U A003277 123,127,131,133,137,139,141,143,145,149,151,157,159,161,163,167,173
%N A003277 Cyclic numbers: n such that n and phi(n) are relatively prime; also n 
               such that there is just one group of order n, i.e. A000001(n) = 1.
%C A003277 Except for a(2)=2, all the terms in the sequence are odd. This is because 
               of the existence of a non-cyclic dihedral group of order 2n for each 
               n>1. - Ahmed Fares (ahmedfares(AT)my-deja.com), May 09 2001
%C A003277 Also GCD[n, A051593[n]] = 1 (Labos E.).
%C A003277 n such that x^n==1 (mod n) has no solution 2<=x<=n - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               May 10 2002
%C A003277 There is only one group (the cyclic group of order n) whose order is 
               n. - Gerard P. Michon (g.michon(AT)att.net), Jan 08 2008
%C A003277 Any divisor of a Carmichael number (A002997) must be odd and cyclic. 
               Conversely, G. P Michon conjectured (c. 1980) that any odd cyclic 
               number has at least one Carmichael multiple (if the conjecture is 
               true, each of them has infinitely many such multiples). In 2007, 
               Michon & Crump produced explicit Carmichael multiples of all odd 
               cyclic numbers below 10000 (see link). - Gerard P. Michon (g.michon(AT)att.net), 
               Jan 08 2008
%D A003277 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 840.
%D A003277 P. Erdos, Some asymptotic formulas in number theory. J. Indian Math. 
               Soc. (N.S.) 12, (1948). 75-78.
%D A003277 J. Pakianathan and K. Shankar, Nilpotent numbers, Amer. Math. Monthly, 
               107 (Aug. 2000), 631-634.
%D A003277 J. S. Rose, A Course on Group Theory, Camb. Univ. Press, 1978, see p. 
               7.
%D A003277 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A003277 T. D. Noe, <a href="b003277.txt">Table of n, a(n) for n = 1..10000</a>
%H A003277 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A003277 Max Alekseyev, <a href="http://garden.irmacs.sfu.ca/?q=op/does_every_odd_number_coprime_to_its_euler_totient_\
               divides_some_carmichael_number">Michon's conjecture</a> (Open Problem 
               Garden, Aug. 2007).
%H A003277 Gerard P. Michon, <a href="http://www.numericana.com/answer/modular.htm#carmdiv">
               Carmichael Divisors</a>
%H A003277 G. P. Michon and J. K. Crump, <a href="http://www.numericana.com/data/
               crump.htm">Carmichael Multiples of Odd Cyclic Numbers</a> (up to 
               10000)
%F A003277 n = p_1*p_2*...*p_k (for some k >= 0), where the p_i are distinct primes 
               and no p_j-1 is divisible by any p_i.
%Y A003277 Cf. A000010, A009195, A050384 (the same sequence but with the primes 
               removed). Also A000001(n) = 1.
%Y A003277 Cf. A002997 A054395.
%Y A003277 Cf. A000001, A003277, A054395, A054396, A054397, A135850.
%Y A003277 Sequence in context: A090421 A102553 A069161 this_sequence A117287 A121615 
               A097605
%Y A003277 Adjacent sequences: A003274 A003275 A003276 this_sequence A003278 A003279 
               A003280
%K A003277 nonn,nice,easy
%O A003277 1,2
%A A003277 N. J. A. Sloane (njas(AT)research.att.com) and R. P. Stanley
%E A003277 More terms from Christian G. Bower (bowerc(AT)usa.net).