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A004169 Values of n for which a regular polygon with n sides cannot be constructed with ruler and compass. 12
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

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 183.

C. F. Gauss, Disquisitiones Arithmeticae, 1801. English translation: Yale University Press, New Haven, CT, 1966, p. 460.

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.

FORMULA

a(n) = n + O(log^2 n). - Charles R Greathouse IV, Oct 23 2015

MATHEMATICA

Select[ Range[75], !IntegerQ[ Log[2, EulerPhi[#] ] ]& ] (* Jean-Fran├žois 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 * A066669 A059808 A020742

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 August 21 16:08 EDT 2017. Contains 290890 sequences.