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 A004169 Values of n for which a regular polygon with n sides cannot be constructed with ruler and compass. 13
 7, 9, 11, 13, 14, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 86, 87, 88, 89, 90, 91 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers m for which phi(a(m)) is not a power of 2, phi = A000010, Euler's totient function. - Reinhard Zumkeller, Jul 31 2012 Numbers m for which A295660(m) > 1. - Lorenzo Sauras Altuzarra, Nov 04 2018 REFERENCES A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 183. B. L. van der Waerden, Modern Algebra. Unger, NY, 2nd ed., Vols. 1-2, 1953, Vol. 1, p. 187. LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 C. F. Gauss, Disquisitiones Arithmeticae, Lipsiae, 1801. Reprinted in C. F. Gauss, Werke, 1863. C. F. Gauss, Disquisitiones Arithmeticae, 1801. English translation: Yale University Press, New Haven, CT, 1966, p. 460. FORMULA a(n) = n + O(log^2 n). - Charles R Greathouse IV, Oct 23 2015 MATHEMATICA Select[ Range[75], !IntegerQ[ Log[2, EulerPhi[#] ] ]& ] (* Jean-François Alcover, Nov 24 2011, after A003401 *) PROG (Haskell) a004169 n = a004169_list !! (n-1) a004169_list = map (+ 1) \$ elemIndices 0 \$ map a209229 a000010_list -- Reinhard Zumkeller, Jul 31 2012 (PARI) is(n)=my(t=4294967295); n>>=valuation(n, 2); n/=gcd(n, t); if(gcd(n, t)>1, return(1)); if(n==1, return(0)); if(n<9e2585827972, return(1)); forprime(p=7, 1e5, if(n%p==0, return(1))); warning("Result is conjectural on the nonexistence of Fermat primes >= F(33)."); 1 \\ Charles R Greathouse IV, Oct 23 2015 CROSSREFS Cf. A003401 (complement). Cf. A000010, A209229. Edge lengths of nonconstructible n-gons: A272487 (n=7), A272488 (n=9), A272489 (n=11), A272490 (n=13), A255241 (n=14), A130880 (n=18), A272491 (n=19). Sequence in context: A262536 A161992 A167377 * A295299 A066669 A059808 Adjacent sequences:  A004166 A004167 A004168 * A004170 A004171 A004172 KEYWORD nonn,nice AUTHOR N. J. A. Sloane, Branislav Kisacanin (bkisacan(AT)eecs.uic.edu) STATUS approved

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Last modified October 23 03:21 EDT 2019. Contains 328335 sequences. (Running on oeis4.)