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%I A003401 M0505
%S A003401 1,2,3,4,5,6,8,10,12,15,16,17,20,24,30,32,34,40,48,51,60,64,68,80,85,96,
%T A003401 102,120,128,136,160,170,192,204,240,255,256,257,272,320,340,384,408,480,
%U A003401 510,512,514,544,640,680,768,771,816,960,1020,1024,1028,1088,1280,1285
%N A003401 Numbers of edges of polygons constructible with ruler and compass.
%C A003401 The terms 1 and 2 correspond to degenerate polygons.
%C A003401 These are also the numbers for which phi(n) is a power of 2.
%D A003401 A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, 
               p. 183.
%D A003401 Allan Clark, Elements of Abstract Algebra, Chapter 4, Galois Theory, 
               Dover Publications, NY 1984, page 124.
%D A003401 C. F. Gauss, Disquisitiones Arithmeticae, 1801. English translation: 
               Yale University Press, New Haven, CT, 1966, p. 460.
%D A003401 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003401 B. L. van der Waerden, Modern Algebra. Unger, NY, 2nd ed., Vols. 1-2, 
               1953, Vol. 1, p. 187.
%H A003401 T. D. Noe, <a href="b003401.txt">Table of n, a(n) for n=1..2000</a>
%H A003401 T. Chomette, <a href="http://www.dma.ens.fr/culturemath/maths/pdf/geometrie/
               polygones.pdf">Construction des polygones reguliers</a>
%H A003401 Bruce Director, <a href="http://www.geocities.com/antidummy/sub/measurement.html">
               Measurement and Divisibility</a>.
%H A003401 C. F. Gauss, <a href="http://134.76.163.65/servlet/digbib?template=view.html&id=38913&startpage=5&endpage=5&i\
               mage-path=http://134.76.176.141:80/cgi-bin/letgifsfly.cgi&image-subpath=1614&pagenumber=5&imageset-id=161\
               4">Disquisitiones Arithmeticae</a>, Lipsiae, 1801. Reprinted in C. 
               F. Gauss, <a href="http://134.76.163.65/agora_docs/38910TABLE_OF_CONTENTS.html">
               Werke</a>, 1863.
%H A003401 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               RegularPolygon.html">Link to a section of The World of Mathematics.</
               a>
%H A003401 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TrigonometricAngles.html">Link to a section of The World of Mathematics.</
               a>
%H A003401 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Trigonometry.html">Link to a section of The World of Mathematics.</
               a>
%H A003401 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TrigonometryAngles.html">Trigonometry Angles</a>
%H A003401 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               ConstructiblePolygon.html">Constructible Polygon</a>
%F A003401 Computable as numbers such that cototient-of-totient equals the totient-of-totient: 
               Flatten[Position[Table[co[eu[n]]-eu[eu[n]], {n, 1, 10000}], 0]] eu[m]=EulerPhi[m], 
               co[m]=m-eu[m]. - Labos E. (labos(AT)ana.sote.hu), Oct 19 2001
%F A003401 Any product of 2^k and distinct Fermat primes (primes of the form 2^(2^m)+1). 
               - Sergio Pimentel (ferdiego(AT)cox-internet.com), Apr 30 2004, edited 
               by Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 16 2006
%e A003401 34 is a term of this series because a circle can be divided exactly in 
               34 parts. 7 is not.
%t A003401 Select[ Range[ 1300 ], IntegerQ[ Log[ 2, EulerPhi[ # ] ] ]& ]
%t A003401 (* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) Take[ 
               Union[ Flatten[ NestList[2# &, Times @@@ Table[ UnrankSubset[n, Join[{1}, 
               Table[2^2^i + 1, {i, 0, 4}]]], {n, 63}], 11]]], 60] (from Robert 
               G. Wilson v (rgwv(AT)rgwv.com), Jun 11 2005)
%Y A003401 Cf. A004169.
%Y A003401 Cf. A000215, A099884.
%Y A003401 Sequence in context: A144043 A121492 A078931 this_sequence A064481 A067939 
               A067784
%Y A003401 Adjacent sequences: A003398 A003399 A003400 this_sequence A003402 A003403 
               A003404
%K A003401 nonn,nice
%O A003401 1,2
%A A003401 N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy
%E A003401 Comment and program from Olivier Gerard (02/99).

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