A117885 Numbers n such that a regular (n^3-n)-gon can be constructed by means of a ruler and compass.

2, 3, 4, 5, 16, 256, 65536

Offset

1,1

Comments

Gauss shows a regular n-gon can be constructed (with Euclidean tools) iff n is a product of 2^k*(distinct Fermat primes).

Links

Table of n, a(n) for n=1..7.

Formula

n^3 - n = (n-1)*n*(n+1).

Example

a(1)=2 because 2^3 - 2 = 6 = 1*2*3, and a regular hexagon can be constructed by ruler and compass.

Prog

(PARI) for(n=1, 10^4, nn= n^3-n; my(t=eulerphi(nn)); if(t/2^valuation(t, 2)==1, print1(n, ", "))); \\ after PARI in A003401; Michel Marcus, Oct 11 2017

Crossrefs

Cf. A003401.

Sequence in context: A293824 A095181 A240906 * A030574 A325652 A283653

Adjacent sequences: A117882 A117883 A117884 * A117886 A117887 A117888

Keyword

nonn,fini,full

Author

Donald S. McDonald, May 02 2006

Status

approved