A004169 Values of m for which a regular polygon with m sides cannot be constructed with ruler and compass.

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

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

Claudi Alsina and Roger B. Nelson, A Panoply of Polygons, Dolciani Math. Expeditions Vol. 58, AMS/MAA (2023), see page 16.

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: A334102 A167377 A360796 * 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